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At least 163 records · Page 9

Double diffusive convection during directional solidification - Nonlinear analysis

The dynamics of doubly diffusive convective flow during the constant-velocity vertical solidification of binary melts to form single-phase solids is examined, summarizing the results of recent experimental and analytical investigations. The effects of horizontal temperature gradients are considered; the nonlinearities of the system and their numerical treatment are discussed; and numerical results are presented graphically for the solidification of a Pb melt containing 0.0015 wt pct Sn, with growth velocity 0.0002 cm/s and a temperature gradient of 200 K/cm in the liquid.

Coriell, S. R.↗

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Wu, Jie↗

A Robust Initialization Scheme for a Lateral Trajectory Optimization Problem with Time of Arrival Windows

We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.

lateral trajectory optimization↗

A self-consistent two-dimensional resistive fluid theory of field-aligned potential structures including charge separation and magnetic and velocity shear

A self-consistent two-fluid theory that includes the magnetic field and shear patterns is developed to model stationary electrostatic structures with field-aligned potential drops. Shear flow is also included in the theory since this seems to be a prominent feature of the structures of interest. In addition, Ohmic dissipation, a Hall term, and pressure gradients in a generalized Ohm's law, modified for cases without quasi-neutrality, are included. In the analytic theory, the electrostatic force is balanced by field-aligned pressure gradients (i.e., thermal effects in the direction of the magnetic field) and by pressure gradients and magnetic stresses in the perpendicular direction. Within this theory, simple examples of applications are presented to demonstrate the kind of solutions resulting from the model. The results show how the effects of charge separation and shear in the magnetic field and the velocity can be combined to form self-consistent structures such as are found to exist above the aurora, suggested also in association with solar flares.

Hesse, Michael↗

The Hadley and Rossby regimes in a spherical atmosphere

The properties of the steady Hadley and Rossby regimes for a thermally forced rotating fluid on a sphere are studied. The two layer modified geostrophic model is employed which allows for thermal advection by the divergent wind and time dependent static stability. Heating processes are parameterized using the Newtonian approximation and Rayleigh friction is accounted for. The equations are transformed to spectral form using spherical harmonics and then truncated retaining a simple axisymmetric state and initial, one wave. A time independent Hadley circulation is obtained which is neutral to axisymmetric disturbances but unstable to wave like perturbations for intermediate values of the meridional temperature gradient, indicating the existence of both an upper and lower symmetric Hadley regime. An analytical solution for the steady Rossby circulation is determined for values of the meridional temperature gradient where the Hadley regime is unstable. Linear perturbation theory is used to show that within the steady Rossby regime two or more waves cannot exist simultaneously.

Feldstein, S. B.↗

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

42 ENGINEERING↗

Development and application of a gradient method for solving differential games

A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.

Roberts, D. A.↗

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗

Consequences of a chromospheric temperature gradient on the width of H Alpha in late-type giants

An analytic expression for the integrated H alpha optical depth profile is derived for a one dimensional slab geometry model chromosphere, with electron temperature increasing as a power law with height. The formula predicts H alpha opacity and profile width to be sensitive functions of the thermal gradient. Application of the model to observation reveals that broad H alpha absorption widths in G and K giant stars are consistent with a mean H alpha chromospheric optical depth of 50, while narrower widths in M stars indicate slightly lower opacities. It is proposed that differences in H alpha width between late-type giants of similar spectral type may be due, in part, to differences in their chromospheric thermal gradient, and associated H alpha opacity.

Zarro, D. M.↗

Structural analysis of cylindrical thrust chambers, volume 2

Analytical results are presented which predict cumulative plastic deformation characteristic of damage observed in coolant channel walls of regeneratively cooled rocket thrust chambers. The damage consists of bulging and plastic flow which leads to thinout and rupture of the channel wall under the combined effects of high pressures, high temperatures and temperature gradients experienced during cyclic firings of actual test chambers. Analytical predictions correlate with test results.

Armstrong, W. H.↗

The evolution of composition and morphology during the initial growth of electrodeposited Ni-Fe films: Comparison between the potentiostatic mode and the pulse-reverse potential mode

The anomalous codeposition of Ni-Fe tends to develop a composition gradient zone along the growth direction within the near-substrate region. Although it has been shown that such a composition gradient can be mitigated by the pulsed deposition method, a fundamental understanding of this behavior based on the anomalous codeposition mechanism has not been achieved yet. In this work, the evolution of the composition and the morphology during the (pulsed) electrodeposition of Ni-Fe films was reported. Further, a theory based on the Fe deposition mechanism originally described by Bockris, Drazic, and Despic was proposed and described in detail, which was used to rationalize not only the occurrence and the decline of the composition gradient, but also the opposite signs of the composition gradient observed under the potentiostatic mode and the pulse-reverse potential mode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Three-Dimensional Viscous Alternating Direction Implicit Algorithm and Strategies for Shape Optimization

A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.

Pandya, Mohagna J.↗

Correlation of analytical and experimental hot structure vibration results

High surface temperatures and temperature gradients can affect the vibratory characteristics and stability of aircraft structures. Aircraft designers are relying more on finite-element model analysis methods to ensure sufficient vehicle structural dynamic stability throughout the desired flight envelope. Analysis codes that predict these thermal effects must be correlated and verified with experimental data. Experimental modal data for aluminum, titanium, and fiberglass plates heated at uniform, nonuniform, and transient heating conditions are presented. The data show the effect of heat on each plate's modal characteristics, a comparison of predicted and measured plate vibration frequencies, the measured modal damping, and the effect of modeling material property changes and thermal stresses on the accuracy of the analytical results at nonuniform and transient heating conditions.

Kehoe, Michael W.↗

Motion of a Drop on a Solid Surface Due to a Wettability Gradient

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.

Subramanian, R.↗

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

OpenMDAO↗

Onset of High-Harmonic Fast Wave Propagation in Annulus Geometry

Previous experiments on NSTX have reported high-harmonic fast wave (HHFW) power losses in the scrape-off layer (SOL), with dependencies on the wave parallel wavenumber, plasma density, and magnetic field. This study presents an analysis of HHFW propagation in the SOL plasma, focusing on parasitic coupling to the waveguide mode bounded by the steep gradient pedestal and the outer wall boundary. The analytic and finite element wave models are discussed using a 2D annulus geometry, which serves as a simplified representation of the NSTX-U plasma. The model shows that a minimum radial gap width is required to support wave propagation, analogous to the higher-order modes in coaxial geometries. The impact of several factors, including gap width, wave parallel phasing, and magnetic field strength, on parasitic wave coupling is examined, highlighting the role of the geometric dimension in relation to the wave perpendicular wavelength. The findings suggest that controlling the edge/SOL density profile (gap control) is crucial for mitigating parasitic coupling when the density in front of the antenna exceeds the density cutoff.

Baek, Seung-Gyou [Massachusetts Inst. of Technolog↗

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β 2 and triaxiality γ. The deformation can be accessed in high-energy heavy ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ε 2 and the density gradient d ⊥ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances $\langleε^{2}_{2}\rangle$ or $\langle$(δd ⊥ /d ⊥ ) 2 $\rangle$ and skewnesses $\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$ or $\langle(δd_{⊥}/d_{⊥})^{3}\rangle$ have a simple analytical form of a'+b'β$^{2}_{2}$ and a'+[b'+c' cos(3γ)]β$^{3}_{2}$, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β 2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β 2 and γ. Assuming a linear relation with elliptic flow v 2 and mean-transverse momentum [p T ] of final-state particles, v 2 ∝ ε 2 and δ [p T ] / [p T ] ∝ δd ⊥ /d ⊥ , similar conclusions are also expected for the variances and skewnesses of v 2 and [p T ], i.e., a + bβ$^{2}_{2}$ for $\langle v^{2}_{2}\rangle$ and $\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$ and a + [b + c cos (3γ)] β$^{3}_{2}$ for $\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$ or $\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos (3γ) ≈ 1, and near oblate nuclei, cos (3γ) ≈ –1 , with known β 2 values, followed by collisions of other species of interest with similar mass number. The (β 2 , γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗