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NASA NTRS2013

Long Hole Film Cooling Dataset for CFD Development : Infrared Thermography and Thermocouple Surveys - Part 1

An experiment investigating flow and heat transfer of long (length to diameter ratio of 18) cylindrical film cooling holes has been completed. In this paper, the thermal field in the flow and on the surface of the film cooled flat plate is presented for nominal freestream turbulence intensities of 1.5 and 8 percent. The holes are inclined at 30deg above the downstream direction, injecting chilled air of density ratio 1.0 onto the surface of a flat plate. The diameter of the hole is 0.75 in. (0.01905 m) with center to center spacing (pitch) of 3 hole diameters. Coolant was injected into the mainstream flow at nominal blowing ratios of 0.5, 1.0, 1.5, and 2.0. The Reynolds number of the freestream was approximately 11,000 based on hole diameter. Thermocouple surveys were used to characterize the thermal field. Infrared thermography was used to determine the adiabatic film effectiveness on the plate. Hotwire anemometry was used to provide flowfield physics and turbulence measurements. The results are compared to existing data in the literature. The aim of this work is to produce a benchmark dataset for Computational Fluid Dynamics (CFD) development to eliminate the effects of hole length to diameter ratio and to improve resolution in the near-hole region. In this report, a Time-Filtered Navier Stokes (TFNS), also known as Partially Resolved Navier Stokes (PRNS), method that was implemented in the Glenn-HT code is used to model coolant-mainstream interaction. This method is a high fidelity unsteady method that aims to represent large scale flow features and mixing more accurately.

Shyam, Vikram↗

NASA NTRS2014

Long Hole Film Cooling Dataset for CFD Development - Flow and Film Effectiveness

An experiment investigating flow and heat transfer of long (length to diameter ratio of 18) cylindrical film cooling holes has been completed. In this paper, the thermal field in the flow and on the surface of the film cooled flat plate is presented for nominal freestream turbulence intensities of 1.5 and 8 percent. The holes are inclined at 30 deg above the downstream direction, injecting chilled air of density ratio 1.0 onto the surface of a flat plate. The diameter of the hole is 0.75 in. (approx. 0.02 m) with center to center spacing (pitch) of 3 hole diameters. Coolant was injected into the mainstream flow at nominal blowing ratios of 0.5, 1.0, 1.5, and 2.0. The Reynolds number of the freestream was approximately 11,000 based on hole diameter. Thermocouple surveys were used to characterize the thermal field. Infrared thermography was used to determine the adiabatic film effectiveness on the plate. Hotwire anemometry was used to provide flowfield physics and turbulence measurements. The results are compared to existing data in the literature. The aim of this work is to produce a benchmark dataset for Computational Fluid Dynamics (CFD) development to eliminate the effects of hole length to diameter ratio and to improve resolution in the near-hole region. In this report, a Time Filtered Navier Stokes (TFNS), also known as Partially Resolved Navier Stokes (PRNS), method that was implemented in the Glenn-HT code is used to model coolant-mainstream interaction. This method is a high fidelity unsteady method that aims to represent large scale flow features and mixing more accurately.

Shyam, Vikram↗

NASA NTRSDate not supplied

Real-Time State Estimation of Structural Modes for an Aeroelastic Wind Tunnel Model

A method is presented for estimating displacements, velocities, and accelerations of structural modes in generalized coordinates from measured sensor data in real time. Specifically, strain data from conventional strain gauges and fiber optic strain sensors (FOSS) were combined with the strain modes (obtained from a finite element model) in a least-squares estimator to produce structural mode displacement estimates and uncertainties. Likewise, accelerometer data were combined with displacement mode shapes in a second least-squares estimator to produce structural mode acceleration estimates. A Kalman filter was then used to refine the displacement estimates and obtain velocity estimates. The method was applied to the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. The technique was found to be useful for real-time control and system identification applications.

Jared A. Grauer↗

NASA NTRS1973

Image enhancement by holography.

The speed of the holographic image deblurring method has recently been further enhanced by a new speed in the realization of the powerful holographic image-deblurring filter. The filter makes it possible to carry out the deblurring, in the optical computer used, in times of the order of one second. The experimental achievements using the holographic image-enhancement method are illustrated with examples ranging from out-of-focus or motion-blurred photographs, including 'amateur' photos recorded on Polaroid film, to the sharpening of the best available electron micrographs of viruses. Images recorded with X-rays, notably from rocket-borne photos of the sun, and out-of-focus photographs from cameras in NASA satellites have been similarly deblurred.

Stroke, G. W.↗

NASA NTRS1996

Jet Evolution Visualized and Quantified Using Filtered Rayleigh Scattering

Filtered Rayleigh scattering was utilized as a flow diagnostic in an investigation of a method for enhancing mixing in supersonic jets. The primary objectives of the study were to visualize the effect of vortex generating tabs on supersonic jets, to exact quantitative data from these planar visualizations, and to detect the presence of secondary flows (i.e., streamwise vorticity) generated by the tabs. An injection seeded frequency-doubled Nd:YAG was the light source and a 14 bit Princeton Instruments iodine charge coupled display (ICCD) camera recorded the image through an iodine cell. The incident wave length of the laser was held constant for each flow case so that the filter absorbed unwanted background light, but permitted part of the thermally broadened Rayleigh scattering light to pas through. The visualizations were performed for axisymmetric jets (D=1.9 cm) operated at perfectly expanded conditions for Mach 1.0, 1.5, and 2.0. All data were recorded for the jet cross section at x/D=3. One hundred instantaneous images were recorded and averaged for each case, with a threshold set to eliminate unavoidable particulate scattering. A key factor in these experiments was that the stagnation air was heated such that the expansion of the flow in the nozzle resulted in the static temperature in the jet being equal to the ambient temperature, assuming isentropic flow. Since the thermodynamic conditions of the flow were approximately the same for each case, increases in the intensity recorded by the ICCD camera could be directly attributed to the Doppler shift, and hence velocity. Visualizations were performed for Mach 1.5 and Mach 2.0 jets with tabs inserted at the nozzle exit. The distortion of the jet was readily apparent and was consistent with Mie scattering-based visualizations. Asymmetry in the intensities of the images indicate the presence of secondary flow patterns which are consistent with the streamwise vortices measured using more traditional diagnostics in subsonic jets with the same tab configurations. Because each tab causes shocks to form, the assumption of isentropic flow is not valid for these cases. However, within a reasonable first-order estimation,the intensity across the illuminated plane for these cases can be related to a value combining density and velocity.

Reeder, Mark F.↗

NASA NTRS1973

Flight results from a study of aided inertial navigation applied to landing operations

An evaluation is presented of the approach and landing performance of a Kalman filter aided inertial navigation system using flight data obtained from a series of approaches and landings of the CV-340 aircraft at an instrumented test area. A description of the flight test is given, in which data recorded included: (1) accelerometer signals from the platform of an INS; (2) three ranges from the Ames-Cubic Precision Ranging System; and (3) radar and barometric altimeter signals. The method of system evaluation employed was postflight processing of the recorded data using a Kalman filter which was designed for use on the XDS920 computer onboard the CV-340 aircraft. Results shown include comparisons between the trajectories as estimated by the Kalman filter aided system and as determined from cinetheodolite data. Data start initialization of the Kalman filter, operation at a practical data rate, postflight modeling of sensor errors and operation under the adverse condition of bad data are illustrated.

Mcgee, L. A.↗

NASA NTRS2009

Metal Standards for Waveguide Characterization of Materials

Rectangular-waveguide inserts that are made of non-ferromagnetic metals and are sized and shaped to function as notch filters have been conceived as reference standards for use in the rectangular- waveguide method of characterizing materials with respect to such constitutive electromagnetic properties as permittivity and permeability. Such standards are needed for determining the accuracy of measurements used in the method, as described below. In this method, a specimen of a material to be characterized is cut to a prescribed size and shape and inserted in a rectangular- waveguide test fixture, wherein the specimen is irradiated with a known source signal and detectors are used to measure the signals reflected by, and transmitted through, the specimen. Scattering parameters [also known as "S" parameters (S11, S12, S21, and S22)] are computed from ratios between the transmitted and reflected signals and the source signal. Then the permeability and permittivity of the specimen material are derived from the scattering parameters. Theoretically, the technique for calculating the permeability and permittivity from the scattering parameters is exact, but the accuracy of the results depends on the accuracy of the measurements from which the scattering parameters are obtained. To determine whether the measurements are accurate, it is necessary to perform comparable measurements on reference standards, which are essentially specimens that have known scattering parameters. To be most useful, reference standards should provide the full range of scattering-parameter values that can be obtained from material specimens. Specifically, measurements of the backscattering parameter (S11) from no reflection to total reflection and of the forward-transmission parameter (S21) from no transmission to total transmission are needed. A reference standard that functions as a notch (band-stop) filter can satisfy this need because as the signal frequency is varied across the frequency range for which the filter is designed, the scattering parameters vary over the ranges of values between the extremes of total reflection and total transmission. A notch-filter reference standard in the form of a rectangular-waveguide insert that has a size and shape similar to that of a material specimen is advantageous because the measurement configuration used for the reference standard can be the same as that for a material specimen. Typically a specimen is a block of material that fills a waveguide cross-section but occupies only a small fraction of the length of the waveguide. A reference standard of the present type (see figure) is a metal block that fills part of a waveguide cross section and contains a slot, the long dimension of which can be chosen to tailor the notch frequency to a desired value. The scattering parameters and notch frequency can be estimated with high accuracy by use of commercially available electromagnetic-field-simulating software. The block can be fabricated to the requisite precision by wire electrical-discharge machining. In use, the accuracy of measurements is determined by comparison of (1) the scattering parameters calculated from the measurements with (2) the scattering parameters calculated by the aforementioned software.

Lambert, Kevin M.↗

NASA NTRS1993

Method of implementing digital phase-locked loops

In a new formulation for digital phase-locked loops, loop-filter constants are determined from loop roots that can each be selectively placed in the s-plane on the basis of a new set of parameters, each with simple and direct physical meaning in terms of loop noise bandwidth, root-specific decay rate, or root-specific damping. Loops of first to fourth order are treated in the continuous-update approximation (BLT yields 0) and in a discrete-update formulation with arbitrary BLT. Deficiencies of the continuous-update approximation in large-BLT applications are avoided in the new discrete-update formulation. A new method for direct, transient-free acquisition with third- and fourth-order loops can improve the versatility and reliability of acquisition with such loops.

Stephens, Scott A.↗

NASA NTRS2011

Orbit Determination of Spacecraft in Earth-Moon L1 and L2 Libration Point Orbits

The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.

Woodard, Mark↗

NASA NTRSDate not supplied

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗

NASA NTRS1979

A model for testing centerfinding algorithms for automated optical navigation

An efficient software simulation of the imaging process for optical navigation is presented, illustrating results using simple examples. The problems of image definition and optical system modeling, including ideal image containing features and realistic models of optical filtering performed by the entire camera system, are examined. A digital signal processing technique is applied to the problem of developing methods of automated optical navigation and the subsequent mathematical formulation is presented. Specific objectives such as an analysis of the effects of camera defocusing on centerfinding of planar targets, addition of noise filtering to the algorithm, and implementation of multiple frame capability were investigated.

Griffin, M. D.↗

NASA NTRS1999

Some Continuum Aspects of Data Assimilation

A long-sought goal in data assimilation is to build more fully the time dimension into the data assimilation process. Truly four-dimensional data assimilation requires evolving second-moment information, namely the estimation error covariance, along with the state estimate itself. The continuum evolution equations for the estimation error covariance constitute a system of partial differential equations in six space dimensions, forced by a model error covariance and by the observations themselves. The high dimensionality of this system poses a difficult computational problem. Numerous methods have been proposed for approximate, discrete solution of this system of equations. Four-dimensional variational schemes solve these equations indirectly, while schemes based on Kalman filtering solve the equations more directly, usually on a small subspace of the full six-dimensional space. In both cases, most proposed solution methods are not derived from the continuum covariance evolution equations themselves. Instead, most methods simply inherit the discretization used for evolving the state estimate, either in the form of a discrete tangent linear model or, in the case of ensemble schemes, in the form of a fully nonlinear discrete model. In this lecture we show that solutions of the continuum covariance evolution equations possess simple properties that are not readily satisfied upon discretization of the equations. we give numerical examples illustrating that "inherited" discretizations sometimes fail to produce meaningfully accurate solutions. Finally, we suggest alternative discretization methods that may yield more faithful approximate solutions of the continuum problem.

Cohn, Stephen E.↗

NASA NTRS1992

A data fusion algorithm for multi-sensor microburst hazard assessment

A recursive model-based data fusion algorithm for multi-sensor microburst hazard assessment is described. An analytical microburst model is used to approximate the actual windfield, and a set of 'best' model parameters are estimated from measured winds. The winds corresponding to the best parameter set can then be used to compute alerting factors such as microburst position, extent, and intensity. The estimation algorithm is based on an iterated extended Kalman filter which uses the microburst model parameters as state variables. Microburst state dynamic and process noise parameters are chosen based on measured microburst statistics. The estimation method is applied to data from a time-varying computational simulation of a historical microburst event to demonstrate its capabilities and limitations. Selection of filter parameters and initial conditions is discussed. Computational requirements and datalink bandwidth considerations are also addressed.

Wanke, Craig R.↗

NASA NTRS1994

A data fusion algorithm for multi-sensor microburst hazard assessment

Wanke, Craig R.↗

NASA NTRS1987

Variability analysis in low count rate sources

A method, based on the chi-square statistics, is described for detecting pulselike time variability in low count rate sources observed with photon-counting instruments. This method can be used even in the presence of observational gaps, takes full advantage of the filtering effect due to binning with different bin sizes, and takes into account the arbitrariness introduced by the binning phase. The procedure developed to limit the dependence of the results on the binning phase and ensure statistically correct results is described along with the application of the proposed procedure to a model of a variable source. Monte Carlo simulations are used to show how the method can be used to derive the characteristic variability time scales and that the method is more sensitive than the nonparametric Kolmogorov-Smirnov test in detecting variability to a given confidence level.

Collura, A.↗

NASA NTRS1995

Investigation of cleanliness verification techniques for rocket engine hardware

Oxidizer propellant systems for liquid-fueled rocket engines must meet stringent cleanliness requirements for particulate and nonvolatile residue. These requirements were established to limit residual contaminants which could block small orifices or ignite in the oxidizer system during engine operation. Limiting organic residues in high pressure oxygen systems is particularly important. The current method of cleanliness verification used by Rocketdyne requires an organic solvent flush of the critical hardware surfaces. The solvent is filtered and analyzed for particulate matter, followed by gravimetric determination of the nonvolatile residue (NVR) content of the filtered solvent. The organic solvents currently specified for use (1,1,1-trichloroethane and CFC-113) are ozone-depleting chemicals slated for elimination by December 1995. A test program is in progress to evaluate alternative methods for cleanliness verification that do not require the use of ozone-depleting chemicals and that minimize or eliminate the use of solvents regulated as hazardous air pollutants or smog precursors. Initial results from the laboratory test program to evaluate aqueous-based methods and organic solvent flush methods for NVR verification are provided and compared with results obtained using the current method. Evaluation of the alternative methods was conducted using a range of contaminants encountered in the manufacture of rocket engine hardware.

Fritzemeier, Marilyn L.↗

NASA NTRS1994

Investigation of Cleanliness Verification Techniques for Rocket Engine Hardware

Oxidizer propellant systems for liquid-fueled rocket engines must meet stringent cleanliness requirements for particulate and nonvolatile residue. These requirements were established to limit residual contaminants which could block small orifices or ignite in the oxidizer system during engine operation. Limiting organic residues in high pressure oxygen systems, such as in the Space Shuttle Main Engine (SSME), is particularly important. The current method of cleanliness verification for the SSME uses an organic solvent flush of the critical hardware surfaces. The solvent is filtered and analyzed for particulate matter followed by gravimetric determination of the nonvolatile residue (NVR) content of the filtered solvent. The organic solvents currently specified for use (1, 1, 1-trichloroethane and CFC-113) are ozone-depleting chemicals slated for elimination by December 1995. A test program is in progress to evaluate alternative methods for cleanliness verification that do not require the use of ozone-depleting chemicals and that minimize or eliminate the use of solvents regulated as hazardous air pollutants or smog precursors. Initial results from the laboratory test program to evaluate aqueous-based methods and organic solvent flush methods for NVR verification are provided and compared with results obtained using the current method. Evaluation of the alternative methods was conducted using a range of contaminants encountered in the manufacture of rocket engine hardware.

Fritzemeier, Marilyn L.↗

NASA NTRS1997

Computations of Complex Three-Dimensional Turbulent Free Jets

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Wilson, Robert V.↗