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At least 199 records · Page 11

A relaxation technique for the parabolized Navier-Stokes (PNS) equations

A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

Kaul, Upender K.↗

Leading-edge effects on boundary-layer receptivity

Numerical calculations are presented for the incompressible flow over a parabolic cylinder. The computational domain extends from a region upstream of the body downstream to the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity, surface pressure and displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. The response to irrotational time harmonic pulsation of the free-stream is examined. Results for the initial development of the velocity profile and displacement thickness are presented. These calculations will be extended to later times to investigate the initiation of instability waves within the boundary-layer.

Gatski, Thomas B.↗

Heat-transfer distributions on biconics at incidence in hypersonic-hypervelocity He, N2, air, and CO2 flows

Laminar heat-transfer rates were measured on spherically blunted, 13 degrees/F degrees on-axis and bent biconics (fore cone bent 7 degrees upward relative to aft cone) at hypersonic-hypervelocity flow conditions in the Langley Expansion Tube. Freestream velocities from 4.5 to 6.9 km/sec and Mach numbers from 6 to 9 were generated using helium, nitrogen, air, and carbon dioxide test gases, resulting in normal shock density ratios from 4 to 19. Angle of attack, referenced to the axis of the aft cone, was varied from zero to 20 degrees in 4 degree increments. The effect of nose bend, angle of attack, and real-gas phenomena on heating distributions are presented along with comparisons of measurement to prediction from a code which solves the three-dimensional 'parabolized Navier-Stokes' equations.

Miller, C. G.↗

Analysis of turbulent underexpanded jets. I - Parabolized Navier-Stokes model, SCIPVIS

A new computational model (SCIPVIS) is described which predicts the multiple-cell wave/shock structure in underexpanded or overexpanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet-mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility-corrected two-equation turbulence models. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial-marching solution can be obtained. The features of SCIPVIS are reviewed, and calculations are described exhibiting the influence of turbulence modelling, jet temperature, and flight velocity on the jet shock structure.

Dash, S. M.↗

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

Li, Fei↗

Modeling the effects of active wake mixing on wake behavior through large-scale coherent structures

The use of active wake mixing (AWM) to mitigate downstream turbine wakes has created new opportunities for reducing power losses in wind farms. However, many current analytical or semi-empirical wake models do not capture the flow instabilities that are excited through the blade pitch actuation. In this work, we develop a framework, which accounts for the impacts of the large-scale coherent structures and turbulence on the mean flow, for modeling AWM. The framework uses a triple-decomposition approach for the unsteady flow field and models the mean flow and fine-scale turbulence with a parabolized Reynolds-averaged Navier–Stokes (RANS) system. The wave components are modeled using a simplified spatial linear stability formulation that captures the growth and evolution of the coherent structures. Comparisons with high-fidelity large eddy simulations (LESs) of the turbine wakes showed that this framework was able to capture the additional wake mixing and faster wake recovery in the far-wake regions for both the pulse and helix AWM strategies with minimal computational expense. In the near-wake region, some differences are observed in both the RANS velocity profiles and initial growth of the large-scale structures, which may be due to some simplifying assumptions used in the model.

17 WIND ENERGY↗

Three-dimensional boundary layer stability and transition

Nonparallel and nonlinear stability of a three-dimensional boundary layer, subject to crossflow instability, is investigated using parabolized stability equations (PSEs). Both traveling and stationary disturbances are considered and nonparallel effect on crossflow instability is found to be destabilizing. Our linear PSE results for stationary disturbances agree well with the results from direct solution of Navier-Stokes equations obtained by Spalart (1989). Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble remarkably well with the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in our nonlinear calculations. Nonlinear interaction of the stationary amplitude of the stationary vortex is large as compared to the traveling mode, and the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the traveling mode dominates the downstream development owing to its higher growth rate, and there is a tendency for the stationary mode to be suppressed. The effect of nonlinear wave development on the skin-friction coefficient is also computed.

Malik, M. R.↗

Computation of three-dimensional flows using two stream functions

An approach to compute 3-D flows using two stream functions is presented. The method generates a boundary fitted grid as part of its solution. Commonly used two steps for computing the flow fields are combined into a single step in the present approach: (1) boundary fitted grid generation; and (2) solution of Navier-Stokes equations on the generated grid. The presented method can be used to directly compute 3-D viscous flows, or the potential flow approximation of this method can be used to generate grids for other algorithms to compute 3-D viscous flows. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since for a 3-D flow there is no unique way to define two sets of intersecting stream surfaces to cover the given flow, different types of two sets of intersecting stream surfaces are considered. First, the metric of the (chi, xi, eta) curvilinear coordinate system associated with each type is presented. Next, equations for the steady state transport of mass, momentum, and energy are presented in terms of the metric of the (chi, xi, eta) coordinate system. Also included are the inviscid and the parabolized approximations to the general transport equations.

Greywall, Mahesh S.↗

Mean-flow measurements in a supersonic three-dimensional turbulent boundary layer

Measurements are presented of the mean flow in a supersonic turbulent boundary layer subjected to a constant weak transverse pressure gradient. The temperature and longitudinal velocity and the axial shear stress were only slightly affected by the three-dimensionality but a clearly defined crossflow component appeared, in the manner suggested by theory and confirmed in earlier experiments. The flow deflection angle and transverse-velocity component achieved a self-preserving form so long as the transverse-pressure gradient remained constant, and both achieved a maximum at the sublayer edge; the deflection angle seemed to decrease again between the latter and the surface. An empirical relation was found between the pressure-gradient strength and the maximum in the crossflow, and the dependence of the latter on distance from the surface was used to test analytical crossflow predictions. The data are in general agreement with Van Den Berg's law of the wall. The data also support the so-called parabolic law following a relaxation distance, especially if inviscid gradients are accounted for, and if the normal coordinate is contracted by the compressibility transformation.

Demetriades, A.↗

Exploring EUV Spicules Using 304 Angstrom He II Data from SDO AIA

We present results from a statistical study of He II 304 Angstrom Extreme Ultraviolet (EUV) spicules at the limb of the Sun. We also measured properties of one macrospicule; macrospicules are longer than most spicules, and much broader in width than spicules. We use high-cadence (12 second) and high-resolution (0.6 arcseconds pixels) resolution data from the Atmospheric Imaging Array (AIA) instrument on the Solar Dynamic Observatory (SDO). All of the observed events occurred near the solar north pole, where quiet Sun or coronal hole environments ensued. We examined the maximum lengths, maximum rise velocities, and lifetimes of 33 Extreme Ultraviolet (EUV) spicules and the macrospicule. For the bulk of the Extreme Ultraviolet (EUV) spicules these quantities are, respectively, approximately 10,000-40,000 kilometers, 20-100 kilometers per second, and approximately 100- approximately 1000 seconds. For the macrospicule the corresponding quantities were respectively approximately 60,000 kilometers, approximately 130 kilometers per second, approximately 1800 seconds, which is typical of macrospicules measured by other workers. Therefore macrospicules are taller, longer-lived, and faster than most Extreme Ultraviolet (EUV) spicules. The rise profiles of both the spicules and the macrospicules match well a second-order ("parabolic" ) trajectory, although the acceleration was often weaker than that of solar gravity in the profiles fitted to the trajectories. Our macrospicule also had an obvious brightening at its base at birth, while such brightening was not apparent for the Extreme Ultraviolet (EUV) spicules. Most of the Extreme Ultraviolet (EUV) spicules remained visible during their descent back to the solar surface, although a small percentage of the spicules and the macrospicule faded out before falling back to the surface. Our sample of macrospicules is not yet large enough to determine whether their initiation mechanism is identical to that of Extreme Ultraviolet (EUV) spicules.

spicules↗

Water Vapor Effects on Silica-Forming Ceramics

Silica-forming ceramics such as SiC and Si3N4 are proposed for applications in combustion environments. These environments contain water vapor as a product of combustion. Oxidation of silica-formers is more rapid in water vapor than in oxygen. Parabolic oxidation rates increase with the water vapor partial pressure with a power law exponent value close to one. Molecular water vapor is therefore the mobile species in silica. Rapid oxidation rates and large amounts of gases generated during the oxidation reaction in high water vapor pressures may result in bubble formation in the silica and nonprotective scale formation. It is also shown that silica reacts with water vapor to form Si(OH)4(g). Silica volatility has been modeled using a laminar flow boundary layer controlled reaction equation. Silica volatility depends on the partial pressure of water vapor, the total pressure, and the gas velocity. Simultaneous oxidation and volatilization reactions have been modeled with paralinear kinetics.

Opila, E. J.↗

Experimental Heat Transfer Results and Flow Visualization of Vertical Upflow Boiling in Earth Gravity with Subcooled Inlet Conditions – In Preparation for Experiments Onboard the International Space Station

Since 2012, researchers at the Purdue University Boiling and Two-Phase Flow Laboratory (PU-BTPFL) and NASA Glenn Research Center have been collaborating on a long-term effort to study flow boiling and condensation in microgravity. The ultimate goal has been to develop the Flow Boiling and Condensation Experiment (FBCE) for the International Space Station (ISS). Based on the findings from prior flow boiling experiments both at different orientations in Earth gravity and onboard parabolic flights simulating short durations of microgravity, a final refined experiment design, construction, and operating procedure have been arrived at for long-duration microgravity flow boiling experiments onboard the ISS. This study investigates flow boiling of n-Perfluorohexane with subcooled inlet in a rectangular channel of dimensions 114.6 mm heated length, 2.5 mm width, and 5 mm height. These pre-launch experiments (Mission Sequence Testing) were conducted in vertical upflow orientation in Earth gravity using the same experimental rig that was launched to the ISS in August 2021. The various operating parameters varied are heating configuration (single- and double-sided), mass velocity (180 – 3200 kg/m2s), inlet subcooling (+0 – 32°C, encompassing both highly subcooled and near-saturated inlet conditions), and inlet pressure (119 – 191 kPa). High-speed video flow visualization images are presented to explain the two-phase interfacial physics within the channel’s heated section. Heat transfer results in terms of flow boiling curves, streamwise profiles of wall temperature and heat transfer coefficient, and averaged heat transfer coefficients are analyzed and parametric effects elucidated. Severe temporal thermodynamic equilibrium is observed for near-saturated inlet at very low velocities. Nucleate boiling degradation starts at larger heat fluxes for single-sided heating than double sided at low mass velocities with highly subcooled inlet, and conversely at high mass velocities with near-saturated inlet. Nucleate boiling degradation can be delayed to higher heat fluxes by highly subcooling the inlet and increasing mass velocity. The entire local heat transfer coefficient profiles are degraded at higher heat fluxes for near-saturated inlet, but only the downstream part for highly subcooled inlet. This study also confirmed reliability of the upcoming ISS experimental data for subcooled inlet conditions and the collected Earth-gravity data will be used for comparison against the ISS data.

flow boiling↗

Calculation of viscous supersonic flows over finned bodies

The parabolized Navier-Stokes (PNS) equations are used to calculate the viscous, supersonic flow fields about a six-finned projectile and a generic four-finned missile at angles of attack. Since current computer speeds and storage preclude a fully three-dimensional calculation using the unsteady, Reynolds-averaged, Navier-Stokes equations, the applicability of the PNS equations to the above flow fields is of considerable interest. Two important aspects of the calculation are grid generation and the type of smoothing used to prevent nonphysical solutions. This paper includes a description of the grid-generation process. Results in the form of density contours and velocity vector plots are presented for the two configurations. The applicability of the PNS equations to the complicated flow fields considered is successfully demonstrated.

Rai, M. M.↗

Optimum transfer between hyperbolic asymptotes with turn angle less than the maximum natural turn angle.

The impulsive transfer of minimum characteristic velocity between two given hyperbolic asymptotes associated with a real planet is considered. The constraint of remaining above the surface of the planet introduces a maximum natural turn angle. This divides the problem naively into two categories. The first is the case when the turn angle required by the given asymptotes is less than or equal to the maximum natural turn angle. This is the more reasonable situation for a swingby maneuver, and is the case considered in this paper. The resulting optimal transfers are of five basic types. In boundary conditions space, by far the largest area of transfers are either single impulse transfers or transfers through the parabolic level requiring two finite impulses. In no case has an optimal transfer been found which uses more than two finite impulses and three infinitesimal impulses. Complete results are presented for the case in which the given turn angle is less than or equal to the maximum natural turn angle.

Walton, J. M.↗

Comparison of experimental and computational compressible flow in a S-duct

This paper describes experimental measurements of secondary flow in a constant area, circular cross-section 30-30 deg S-duct, and compares the results obtained with the computations performed using the PEPSIG code, a parabolized Navier-Stokes code. The flow entering the duct was turbulent, with entrance Mach number of 0.6, and the boundary layer thickness at the duct entrance was 10 percent of the duct diameter. The duct mean radius of curvature to the duct diameter was 5.077. Flow parameters were measured at six stations along the length of the duct. These measurements were made using a five-port cone probe. At least ten radial traverses were made at each station on both sides of the symmetry plane. Wall static pressures along three azimuth angles of zero, 90, and 180 deg along the duct were measured. Plots presenting the secondary velocity field as well as contour plots of the total and static-pressure fields have been obtained. Strong secondary flows were observed in the first bend, and these continued into the second bend with the formation of new vorticity in the opposite sense in the second bend. The flow exiting the duct contained two pairs of counter-rotating vortices. The computational results are in general agreement with the experiments. However, it appears that the computations underestimate the extent of the pressure distortion, due to simplifications made in the pressure field calculations.

Vakili, A.↗

Heat-transfer distributions for biconics at incidence in hypersonic-hypervelocity real-gas flows

Laminar heat-transfer distributions were measured on spherically blunted, 13/7 deg straight and bent biconics at freestream velocities from 4.5 to 6.9 km/s and Mach numbers from 6 to 9. The flows were generated in the NASA's Langley Expansion Tube using helium, nitrogen, air, and carbon dioxide; angle of attack, referenced to the axis of the aft cone, was varied from zero to 20 deg. The penalty in windward heating to the fore cone due to the 7-deg nose bend diminished rapidly with increasing angle of attack and was only 10 to 20 percent at the design trim angle of attack of 20 deg. Leeward heating initially decreased, then increased, with increasing angle of attack. Windward heating rates predicted with a computer code that solves the parabolized Navier-Stokes equations were in good agreement with measurements for helium and air. The study used a 1.9-percent scale model of the proposed generic planetary vehicle and is directly applicable to the orbital transfer vehicle, which incorporates a spherically blunted biconic.

Miller, C. G.↗

Computation of three-dimensional inviscid flow over hypersonic missile configurations using the GIM code

A three-dimensional computational technique was used to obtain flowfield solutions to the Euler equations over selected hypersonic missile configurations. The General Interpolants Method (GIM) computer code was used with interpolation functions in an algebraic approach to generate a discrete computational grid for each configuration. The spatial marching version of the GIM code, which treats the parabolized Navier-Stokes (PNS) equations or the Euler equations with a shock capturing, 'MacCormack-like' scheme, was used to advance the solution hyperbolically over each configuration. The inviscid flowfield solutions over the two three-dimensional missile configurations, calculated using the GIM hyperbolic scheme, are presented here. The flow field over a wing/body configuration at zero degree angle of attack is presented. Flow over the fuselage of a tactical missile, termed the TAME 10, at both zero degree and 7.5 degree angles of attack is presented. In addition, an inviscid, two-dimensional analysis of an inlet configuration designed to mount on the TAME 10 is included. Contour maps of velocity and pressure are included for each configuration. Comparison of calculation and data show good agreement.

Xiques, K. E.↗

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m.

Newman, Dava J.↗