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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Saturation effects associated with sound propagation in a turbulent medium

A theoretical analysis of the acoustic wave field radiated by a time-harmonic point source in a homogeneous, isotropic turbulent medium is presented. The smoothing method is used to study the incoherent, or randomly fluctuating, component of the wave field. The analysis considers the effect on the wave of the velocity fluctuations, as well as the index-of-refraction fluctuations, of the medium. An approximate expression for the second moment of the incoherent wave is obtained for the case in which the wavelenght is much less than the minimum correlation length of the medium. This expression shows that the fluctuations of the wave increase initially in proportion to the propagation distance, but that at larger distances they tend to a limiting, or saturation, value. These results agree with observations of waves propagating in real media. It is also found that the mean square of the total (i.e., coherent plus incoherent) acoustic pressure is unaffected by the randomness of the medium.

Wenzel, A. R.↗
NASA NTRS1977

Modelling the effects of turbulence on acoustic wave propagation

A review of recent theoretical modeling of the effects of turbulence on acoustic wave propagation is presented. The Born approximation limit of the smoothing method of Keller and of the kinetic theory method of Howe are compared with the classical perturbation results of Chernov. Secular growth is observed in the higher order terms of the kinetic theory method of Howe when multiple scaling is ignored. The forward propagation - beam broadening model of Brown and Clifford is discussed as well as the single scatter model of DeLoach and of Rudd. Each model is examined with respect to its prediction of conservation of energy.

Harris, W. L.↗
NASA NTRS2014

A One-Dimensional Global-Scaling Erosive Burning Model Informed by Blowing Wall Turbulence

This paper makes no attempt to comprehensively review erosive burning models or the data collected in pursuit of them; the interested reader could begin with Landsbaum for a historical summary. However, a discussion and comparison to recent work by McDonald and Rettenmaier and Heister will be included, along with data generated by Strand, et. al. Suffice it to say that the search for a way to predict erosive burning in any size motor with formulas cleanly applicable to a typical 1D ballistics analysis has been long thwarted. Some models were based on testing that failed to adequately simulate the solid rocket motor environment. In most cases, no real‐time burn rate measurement was available. Two popular models, even when calibrated to recent motor‐like real‐time burn rate data obtained by Furfaro, were shown by McMillin to be inadequate at modeling erosive burning in the Space Shuttle Reusable Solid Rocket Motor (RSRM), the Space Launch Systems' Five‐Segment RSRM (RSRMV), and the five‐segment Engineering Test Motor (ETM)‐3. Subsequently to the data cited from Strand and Furfaro, additional motors of the same kind as Furfaro's were tested with RSRMV propellant, utilizing 7 segments per motor and 3 throat sizes. By measuring propellant web thickness with ultrasonic gages, the burn rate was determined at cross‐flow Mach numbers up to Mach 0.8. Furthermore, because of the different throat sizes in otherwise identical motors, this provides a unique look at the effect of pressure and base burn rate on the erosive response. Figure 1 shows example of the data pertaining to the high Mach motor, where the port area is initially less than the throat area. The burn rate data was processed using a smoothing method developed to reduce the noise without too severely introducing end effects that limit the range of useful data. Then, an empirical ballistics scheme was used to estimate the flow condition based on the burn rate measurements and pressure measured between each segment.

Kibbey, Timothy P.↗
NASA NTRS2008

Development of a Smooth Trajectory Maneuver Method to Accommodate the Ares I Flight Control Constraints

Six degree-of-freedom (DOF) launch vehicle trajectories are designed to follow an optimized 3-DOF reference trajectory. A vehicle has a finite amount of control power that it can allocate to performing maneuvers. Therefore, the 3-DOF trajectory must be designed to refrain from using 100% of the allowable control capability to perform maneuvers, saving control power for handling off-nominal conditions, wind gusts and other perturbations. During the Ares I trajectory analysis, two maneuvers were found to be hard for the control system to implement; a roll maneuver prior to the gravity turn and an angle of attack maneuver immediately after the J-2X engine start-up. It was decided to develop an approach for creating smooth maneuvers in the optimized reference trajectories that accounts for the thrust available from the engines. A feature of this method is that no additional angular velocity in the direction of the maneuver has been added to the vehicle after the maneuver completion. This paper discusses the equations behind these new maneuvers and their implementation into the Ares I trajectory design cycle. Also discussed is a possible extension to adjusting closed-loop guidance.

Pinson, Robin M.↗
NASA NTRS1968

New technique for optimal smoothing of data

Recursive method for the optimal smoothing of data has numerical superiority and is more easily understood in terms of physical reasoning than earlier methods. Using a Kalman filter, the smoothing technique, applied to a nonlinear parameter identification problem, is useful in those situations where linearization about a reference solution is valid.

Fraser, D. C.↗
NASA NTRS1978

Solution of axisymmetric and two-dimensional inviscid flow over blunt bodies by the method of lines

Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.

Hamilton, H. H., II↗
NASA NTRS1990

Surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for Space Station Freedom

The surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for the Space Station Freedom are described. The purpose of the surface definition and grid generation is to provide the necessary geometry information for CFD calculations about the vehicle. There are two salient features in this description. The first is that the numerical model representing the ACRV configuration is obtained from the measurement of an existing wind tunnel model. The method for smoothing the measured data and obtaining the numerical model is described. The second feature is the description of the algebraic grid generation method and software to compute volume grids about the ACRV. The methods and software allow rapid computation of volume grids for a wide range of flow conditions.

Smith, R. E.↗
NASA NTRS1959

Sampled-Data Techniques Applied to a Digital Controller for an Altitude Autopilot

Sampled-data theory, using the Z transformation, is applied to the design of a digital controller for an aircraft-altitude autopilot. Particular attention is focused on the sensitivity of the design to parameter variations and the abruptness of the response, that is, the normal acceleration required to carry out a transient maneuver. Consideration of these two characteristics of the system has shown that the finite settling time design method produces an unacceptable system, primarily because of the high sensitivity of the response to parameter variations, although abruptness can be controlled by increasing the sampling period. Also demonstrated is the importance of having well-damped poles or zeros if cancellation is attempted in the design methods. A different method of smoothing the response and obtaining a design which is not excessively sensitive is proposed, and examples are carried through to demonstrate the validity of the procedure. This method is based on design concepts of continuous systems, and it is shown that if no pole-zero cancellations are allowed in the design, one can obtain a response which is not too abrupt, is relatively insensitive to parameter variations, and is not sensitive to practical limits on control-surface rate. This particular design also has the simplest possible pulse transfer function for the digital controller. Simulation techniques and root loci are used for the verification of the design philosophy.

Schmidt, Stanley F.↗
NASA NTRS1975

Solutions to Kuessner's integral equation in unsteady flow using local basis functions

The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

Fromme, J. A.↗
NASA NTRS2001

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗
NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗
NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗
NASA NTRS1972

Velocity of the solar wind as determined from interplanetary scintillations.

The method of smooth perturbations is used to derive the equations for interplanetary scintillation in a (statistically) spherically symmetric solar wind with constant wind velocity. The expressions, valid in the limit of small scintillation index, are used to discuss the relation between the radial wind velocity and the observed projected velocity of the scintillation pattern. It is found that the pattern velocity is systematically less than the wind velocity by a substantial fraction, depending on the radial variation of the density fluctuations. If the fluctuations fall off as 1/r-squared the correction is 18 percent, whereas if the fluctuations are proportional to 1/r the correction is 57 percent. The effects may be even more severe if the solar wind is not spherically symmetric.

Jokipii, J. R.↗
NASA NTRS1973

Shock-wave structure in a fully ionized gas.

The structure of a steady plane shock in a fully ionized gas has been investigated using the Boltzmann equation with the Gross-Krook type model as the governing equation and the discrete-ordinate method as a tool. The present results agree well with the results obtained by the continuum approach for weak shocks. For strong shocks the present approach gives results that are considerably different from those yielded by the continuum approach, particularly in the high pressure region. Also, the present method gives smooth and continuous shock profiles for high Mach numbers. On the other hand, the results from the continuum approach contain discontinuities in slope. The ion and electron distribution functions across the shock are found to be singly peaked for all cases considered and the effects of the induced electric field is small.

Lu, C. S.↗