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At least 145 records · Page 8

Computations of the Magnus effect for slender bodies in supersonic flow

A recently reported Parabolized Navier-Stokes code has been employed to compute the supersonic flow field about spinning cone, ogive-cylinder, and boattailed bodies of revolution at moderate incidence. The computations were performed for flow conditions where extensive measurements for wall pressure, boundary layer velocity profiles and Magnus force had been obtained. Comparisons between the computational results and experiment indicate excellent agreement for angles of attack up to six degrees. The comparisons for Magnus effects show that the code accurately predicts the effects of body shape and Mach number for the selected models for Mach numbers in the range of 2-4.

Sturek, W. B.

Finite difference procedure for boundary layers including effects of longitudinal and transverse curvatures

A second order viscous layer solution procedure has been developed that does in a consistent way include curvature effects and the corresponding normal pressure gradients. In the present system, the normal momentum equation is retained. The parabolic system of nonlinear partial differential equations is converted by linear finite differencing procedures to a system of linear algebraic equations and solved in primitive coordinates. The solutions have been shown to give smooth stable distributions for all the variables, most particularly the normal velocity which plays an important role in the interaction procedure. An algorithm for matching the viscous layer solution with a rotational characteristics outer solution has been developed.

Tassa, Y.

Experimental Investigation of Flow Condensation in Microgravity

Future manned missions to Mars are expected to greatly increase the space vehicle's size, weight, and heat dissipation requirements. An effective means to reducing both size and weight is to replace single-phase thermal management systems with two-phase counterparts that capitalize upon both latent and sensible heat of the coolant rather than sensible heat alone. This shift is expected to yield orders of magnitude enhancements in flow boiling and condensation heat transfer coefficients. A major challenge to this shift is a lack of reliable tools for accurate prediction of two-phase pressure drop and heat transfer coefficient in reduced gravity. Developing such tools will require a sophisticated experimental facility to enable investigators to perform both flow boiling and condensation experiments in microgravity in pursuit of reliable databases. This study will discuss the development of the Flow Boiling and Condensation Experiment (FBCE) for the International Space Station (ISS), which was initiated in 2012 in collaboration between Purdue University and NASA Glenn Research Center. This facility was recently tested in parabolic flight to acquire condensation data for FC-72 in microgravity, aided by high-speed video analysis of interfacial structure of the condensation film. The condensation is achieved by rejecting heat to a counter flow of water, and experiments were performed at different mass velocities of FC-72 and water and different FC-72 inlet qualities. It is shown that the film flow varies from smooth-laminar to wavy-laminar and ultimately turbulent with increasing FC-72 mass velocity. The heat transfer coefficient is highest near the inlet of the condensation tube, where the film is thinnest, and decreases monotonically along the tube, except for high FC-72 mass velocities, where the heat transfer coefficient is enhanced downstream. This enhancement is attributed to both turbulence and increased interfacial waviness. One-ge correlations are shown to predict the average condensation heat transfer coefficient with varying degrees of success, and a recent correlation is identified for its superior predictive capability, evidenced by a mean absolute error of 21.7%.

microgravity

Low speed airfoil design and analysis

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Eppler, R.

Numerical simulation of steady supersonic flow over spinning bodies of revolution

A recently reported parabolized Navier-Stokes code has been employed to compute the supersonic flowfield about a spinning cone and spinning and nonspinning ogive cylinder and boattailed bodies of revolution at moderate incidence. The computations were performed for flow conditions where extensive measurements for wall pressure, boundary-layer velocity profiles, and Magnus force had been obtained. Comparisons between the computational results and experiment indicate excellent agreement for angles of attack up to 6 deg. At angles greater than 6 deg discrepancies are noted which are tentatively attributed to turbulence modeling errors. The comparisons for Magnus effects show that the code accurately predicts the effects of body shape for the selected models.

Sturek, W. B.

A detailed study of mean-flow solutions for stability analysis of transitional flows

A finite-volume upwind-difference parabolized Navier-Stokes code is utilized to obtain laminar mean-flow solutions at Mach 3.5 on a half-angle cone of 5 deg at an angle-of-attack of 2 deg. A detailed study is conducted on this configuration; the main focus is the velocity profiles in the leeward and windward symmetry planes at various axial locations. Comparisons of the solution profiles are made with both a central-difference code that incorporates scalar and matrix dissipation models and another state-of-the-art upwind-difference finitevolume code. The results obtained emphasize the importance of using matrix dissipation models for schemes that require explicit artificial dissipation. These results also illustrate the accuracy and efficiency of the planeby-plane marching procedure for computing mean-flow solutions for predicting the onset of transition with linear instability.

Ramakrishnan, R.

Convection, nucleosynthesis, and core collapse

We use a piecewise parabolic method hydrodynamics code (PROMETHEUS) to study convective burning in two dimensions in an oxygen shell prior to core collapse. Significant mixing beyond convective boundaries determined by mixing-length theory brings fuel (C-12) into the convective regon, causing hot spots of nuclear burning. Plumes dominate the velocity structure. Finite perturbations arise in a region in which O-16 will be explosively burned to Ni-56 when the star explodes; the resulting instabilities and mixing are likely to distribute Ni-56 throughout the supernova envelope. Inhomogeneities in Y(sub e) may be large enough to affect core collapse and will affect explosive nucleosynthesis. The nature of convective burning is dramatically different from that assumed in one-dimensional simulations; quantitative estimates of nucleosynthetic yields, core masses, and the approach to core collapse will be affected.

Bazan, Grant

Incompressible Navier-Stokes and parabolized Navier-Stokes formulations and computational techniques

The differential formulations and computational techniques currently used for the incompressible Navier-Stokes (NS) and parabolic Navier-Stokes (PNS) equations are reviewed. In particular, attention is given to problems associated with the choice of difference equations, the method of solution and the choice of algorithm, the coupling of dependent variables and discretized equations, the application of boundary conditions, and grid generation. A new composite velocity NS and PNS formulation in (u,v,p) variables is presented, and the applicability of a 'forward' difference global pressure iteration for the (u,v,p) PNS system is demonstrated.

Rubin, S. G.

Zero-G experiments in two-phase fluids flow regimes

The two-phase flows studied were liquid and gas mixtures in a straight flow channel of circular cross-section. Boundaries between flow regimes have been defined for normogravity on coordinates of gas quality and total mass velocity; and, when combined with boundary expressions having a Froude number term, an analytical model was derived predicting boundary shifts with changes in gravity level. Experiments with air and water were performed, first in the normogravity environment of a ground laboratory and then in 'zero gravity' aboard a KC-135 aircraft flying parabolic trajectories. Data reduction confirmed regime boundary shifts in the direction predicted, although the magnitude was a little less than predicted. Pressure drop measurements showed significant increases for the low gravity condition.

Heppner, D. B.

Numerical solution for subcritical flows by a transonic integral equation method

The method presented makes use of a division of the region of integration into closed rectangular elements. The velocity is taken to be constant in each element. The integral equation is reduced to a matrix equation which can be solved by an appropriate iteration approach. The derivation and solution of the matrix equation are discussed and the matrix elements are considered. The described concepts were implemented for a nonlifting parabolic-arc airfoil.

Ogana, W.

Laser-driven flash x-ray radiography of a shocked metallic foil

Characterizing hydrodynamic instability evolution in millimeter-scale, high-Z foils is crucial for understanding complex phenomena in high-energy-density physics. Here, we demonstrate a proof-of-concept, laser-driven flash x-ray radiography platform tailored for two-dimensional linear density mapping in shocked high-Z foils. Using chromium (Cr) foils with internal shockwaves (∼100 μm width), our platform achieves a spatial resolution of 59.8 ± 1.4 μm by employing a broadband x-ray source extending into the hundreds of keV range. The setup combines a compound parabolic concentrator cone with a tantalum wire target, a magnetic field to deflect residual transmitted electrons, and a copper casing to shield the sides and rear of the image plate pack. By varying the delay of the short-pulse beam driving the flash x-ray source, we resolve shockwave dynamics, specifically the velocity, position, width, and density profile, within the Cr foil. Reported experimental results are consistent with the corresponding hydrodynamics and radiation transport simulations, which accurately reproduce the measured electron and x-ray source terms. These developments enable the conversion of shockwave radiographs into two-dimensional density maps, enhancing interpretability for hydrodynamic instability evolution applications and validating the simulation approach.

36 MATERIALS SCIENCE

Calculation of three-dimensional, viscous flow through turbomachinery blade passages by parabolic marching

The three-dimensional compressible Navier-Stokes equations are formulated in a rotating coordinate system, so as to include centrifugal and Coriolis forces. The equations are parabolized by using a previously calculated inviscid static pressure field. The thin layer Navier-Stokes approximation, which neglects streamwise diffusion, is used. A body-fitted coordinate system is used. The streamwise momentum equation is uncoupled from the cross-stream momentum equation by using contravariant momentum components, and then using the contravariant velocity components as primary unknowns. To reduce problems with small separated regions, the Reyhner and Flugge-Lotz approximation is used. The energy equation is included to allow for calculation of heat transfer. The flow may be laminar, or a simple eddy-viscosity turbulence may be used. A number of curved ducts and an axial stator were analyzed, including cases for which experimental data are available.

Katsanis, T.

A space-marching method for incompressible Navier-Stokes equations

This paper deals with the development of a space-marching method for incompressible flows. The method solves the continuity and momentum equations as a coupled system at each streamwise station. The character of the system of equations has been changed from elliptic to hyperbolic/parabolic in order to enable the equations to be marched in space. The present method has many advantages compared to the existing parabolic or space-marching methods for incompressible flow: (1) it avoids the solution of Poisson equations, (2) it conserves the mass flow with no additional computation, (3) it does not require the specification of an assumed pressure field when used in the prediction of duct flows. The present method can capture strong secondary velocities and strong transverse pressure gradients. Predictions of the flow through straight and curved ducts are in good agreement with analytical and experimental results.

Pouagare, M.

Calculation of three-dimensional, viscous flow through turbomachinery blade passages by parabolic marching

The three-dimensional compressible Navier-Stokes equations are formulated in a rotating coordinate system, so as to include centrifugal and Coriolis forces. The equations are parabolized by using a previously calculated inviscid static pressure field. The thin layer Navier-Stokes approximation, which neglects streamwise diffusion, is used. A body-fitted coordinate system is used. The streamwise momentum equation is uncoupled from the cross-stream momentum equation by using contravariant momentum components, and then using the contravariant velocity components as primary unknowns. To reduce problems with small separating regions, the Reyhner and Flugge-Lotz approximation is used. The energy equation is included to allow for calculation of heat transfer. The flow may be laminar, or a simple eddy-viscosity turbulence may be used. A number of curved ducts and an axial stator were analyzed, including cases for which experimental data are available.

Katsanis, T.

Cryogenic Flow Boiling in Microgravity: Effects of Reduced Gravity on Two-Phase Fluid Physics and Heat Transfer

With the growing interest in space exploration, cryogenic technologies involving two-phase flow and heat transfer are in high demand to successfully procure advanced space applications such as fuel depots and nuclear thermal propulsion (NTP) systems for deep space missions. However, the unique and extreme thermal properties of cryogenic fluids introduce distinct flow boiling fluid physics and energy transport phenomena, which differ significantly from those observed with conventional fluids. Understanding the unique two-phase physics in cryogenic flow boiling remains an ongoing challenge. Furthermore, the lack of readily available microgravity cryogenic steady-state heat transfer data hinders the assessment of gravitational effects on cryogenic flow boiling. This study aims to elucidate the gravitational effects on two-phase fluid physics and heat transfer by conducting the first-ever experimental measurement of cryogenic flow boiling performance using a steady-state heated method in a reduced gravity environment. Parabolic flight experiments were performed to acquire both heat transfer measurements and high-speed video of interfacial behaviors, under varying gravity levels (microgravity, hypergravity, Lunar gravity, and Martian gravity). The experiments involved flow boiling of liquid nitrogen (LN 2 ) with a near-saturated inlet along a circular heated tube of dimensions 8.5-mm inner diameter and 680-mm heated length. The operating parameters varied are mass velocity of 398.3 - 1342.8 kg/m2s, inlet quality of -0.08 to -0.01, and inlet pressure of 413.68 - 689.48 kPa. Captured microgravity flow patterns range from bubbly to annular, all having vapor structures that are larger than those under higher gravity levels. Under microgravity, absence of buoyancy yields symmetrical vapor structures without flow stratification, laying a physical foundation for the distinct two-phase heat transfer trends during LN 2 flow boiling in microgravity. Transient data collected during the flight parabolas exhibited decreasing heated wall temperature as the aircraft transitioned from hypergravity to microgravity phases. The temperature variation indicated an enhancement in flow boiling heat transfer with decreasing gravity levels and a reduction with increasing gravity levels. The effect of reduced gravity on cryogenic flow boiling heat transfer coefficient (HTC) is discussed based on steady state heat transfer analysis. Seminal HTC correlations are evaluated against the measured microgravity HTC data, of which one is identified for superior accuracy in predicting microgravity data. Finally, a new HTC correlation is proposed to improve accuracy of microgravity predictions, yet there still exists room for further improvement with future terrestrial flow boiling experiments at different flow orientations relative to Earth gravity.

Microgravity

Application of the method of integral relations to laminar boundary layers in three dimensions

The method of integral relations is extended to general three-dimensional compressible laminar boundary layer flows. The transformation employed to transform the basic three-dimensional compressible boundary layer equations into quasi-incompressible form is an extension of the Howarth transformation. The resulting system of differential equations is integrated numerically by the method of integral relations as proposed by Dorodnitsyn. To demonstrate the accuracy of the method, it is applied to calculation of the parabolic flow over a flat plate and the boundary flow over an infinite yawed cylinder, for which solutions are known. It is then applied to the flow over a flat plate disturbed by a cylinder normal to the plate, for which a finite-difference solution is available for comparison. It is finally applied to calculating the crossflow velocity variation for supersonic flow over a swept wedge.

Holt, M.

Propulsive trajectory optimization to minimize surface contamination

MOTIVATION: We present an optimization technique for propulsive vehicles that autonomously minimizes contamination during surface approach and landing. In addition to short-range hoppers, the optimization technique is also fully applicable to traditional orbit-to-surface landers. This study addresses scenarios where surface alterations from propulsion events are counterproductive or hazardous to the mission objectives. This is of immediate interest for landers (whether human or robotic), that may rely on pristine soils collected in the immediate vicinity of landing sites to accomplish science investigations, mining, or ISRU surface operations. Such missions are averse to various surface-plume interactions such as thermal scoring, physical agitation, and contamination. The capability can be applied with minimal impact to the baseline mission concept. METHODS: Optimization algorithms have been developed to calculate descent trajectories and maneuvers, thrust magnitude, and attitude for various mission cases. These parameters are determined as an optimal solution when minimizing either fuel consumption, contamination deposited at the landing site, or some weighted combination of both. Among constraints imposed on the solution, we examined pitch rate, vertical takeoff and vertical landing (VTVL) requirements, size of the contamination zone, and minimum ground clearance during flight. This tool provides unique, non-intuitive solutions and can be a valuable resource for mission planners. RESULTS: A variety of agile trajectory solutions were obtained, each yielding different reductions in landing site contamination and corresponding to only modest increases in fuel consumption. Several optimal trajectories were obtained by varying the contamination weight in the fitness function. As expected, when the contamination weight is zero, the trajectory appears close to parabolic since the optimization scheme only attempts to minimize for fuel utilization, yielding essentially, the expected ballistic trajectory. Notably for contamination weights greater than zero, trajectory inflections are observed in the descent phase, which manifests as hovering or additional, mini “pseudo hops” before the final touchdown. A trajectory inflection is characterized by arresting the majority of the spacecraft vertical velocity component at a coordinate outside of the landing target, and without violating ground clearance constraints. FUTURE WORK: Our optimization technique is ready for laboratory or field demonstrations to validate the sophisticated maneuvering solutions obtained for fuel optimization and surface preservation. An appropriate testbed would validate the optimal guidance algorithms, the navigation system, and sensor suite by emulating vehicle flight in closed loop robotic tests. Critically, these algorithms could then be ported to flight software for implementation.

surface contamination

Rotation period of comet Donati

Consideration is given to the rotation period of comet Donati (1858 VI) whose haloes were approximate parabolic envelopes having foci near the apparent nucleus and vertices toward the sun forward from the tail axis. The regularity and sharpness of the halves suggest that they represent the repetitive ejection of material from an active area which is exposed to solar radiation as the cometary nucleus rotates. Bobrovnikov's results (1954) are used to evaluate the linear expansion velocity of such haloes. This calculation is applied to the comet and a linear correction is used to assess the results.

Whipple, F. L.