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At least 55 records · Page 3

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O ( N ) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. Further, we work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

SanAndres, Luis↗

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗

Prediction of light aircraft interior sound pressure level from the measured sound power flowing in to the cabin

The validity of the room equation of Crocker and Price (1982) for predicting the cabin interior sound pressure level was experimentally tested using a specially constructed setup for simultaneous measurements of transmitted sound intensity and interior sound pressure levels. Using measured values of the reverberation time and transmitted intensities, the equation was used to predict the space-averaged interior sound pressure level for three different fuselage conditions. The general agreement between the room equation and experimental test data is considered good enough for this equation to be used for preliminary design studies.

Atwal, Mahabir S.↗

A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Response of a confined gas to volumetric heating in the absence of gravity. I - Slow transients

A one-dimensional model for bulk motion induced by a transient volumetric heat source in a confined gas at zero gravity is considered. Rational approximation methods are used to derive a quantitative theory for the gas response to a spatiallly distributed, time-dependent internal power deposition. The resulting low Mach number compressible flow equations are solved by using perturbation methods. Solutions are given for a conduction-free core and thin conductive boundary layers adjacent to the end walls. It is found that may any spatially nonuniform power deposition will cause fluid motion. Net mass transport in the closed container will occur for certain spatially distributed heating. The model mimics the thermal effects of an exothermic gas phase reaction in vapor transport experiments conducted in space. The solutions demonstrate that thermally induced mass transport can be as large as diffusive mass transport in a typical experiment.

Herczynski, A.↗

Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. Here, we investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher↗

Modeled sensitivity of multi-MA accelerator performance to electrode contaminant inventory

Significant particle-in-cell code development has enabled simulations of power flow in multi-MA accelerators to include the desorption of surface contaminants, their ionization into surface plasmas, and the impact of these plasmas on efficiency. The simulations base desorption on an Arrhenius equation, whose most significant unknown is the surface contaminant inventory. The sensitivity of power-flow simulations to this inventory is studied here using Sandia National Laboratories' Z accelerator with a 7-nH MagLIF load [Phys. Plasmas 17, 056303 (2010)]. Simulations are conducted in 3D cylindrical coordinates for the current-adder, or “convolute,” region of Z and in 2D for the final feed only. Simulated contaminant inventories are varied from 1 to 32 monolayers (MLs) in 2D, and 2 to 4 ML in 3D. The results reveal sensitivities to the local ratio of E/B⁠. The high B-field, low E-field region near the short-circuit load is insensitive to the contaminant inventory, where assumed values of 4–32 ML change the load current by ≤ 2%, and agree with experiment to within 2% at peak current. A 1-ML value is the outlier, increasing the load current by 5%, but still within measurement uncertainty. In contrast, the relatively higher E-field, lower B-field convolute region has slower contaminant desorption and higher-magnitude E-field penetration of the surface plasmas. The current loss in the convolute region does increase with contaminant inventory. The loss assuming 4 ML is 12% larger than for 2 ML, with 4 ML being the better match to experiment.

Arrhenius equation↗

Comparison of semikinetic and generalized transport models of the polar wind

A rigorous comparison is made of a semikinetic model and the bi-Maxwellian-based 16-moment transport equations for polar wind conditions. The comparisons show remarkably close agreement in the corresponding predictions for the altitudinal variation of the various plasma parameters. These results indicate that the bi-Maxwellian-based transport equations are a powerful tool for modeling a wide range of thermal plasma flows throughout the solar-terrestrial environment. In the collisionless limit, the results indicate that the 16-moment transport equations are equivalent to the kinetic models commonly used in solar and polar wind studies.

Demars, H. G.↗

Laminar boundary-layer flow of non-Newtonian fluid

A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.

Lin, F. N.↗

Intrinsically asymmetric astrophysical jets

Previous work on the origin of self-collimated electromagnetic jets is extended to the general case where there is no reflection symmetry of the magnetic field about the equatorial plane of the disk. The axisymmetric field structure inside the disk is obtained by solving for the magnetic flux function, and the toroidal magnetic field, from the generalized thin-disk induction equation, which is derived. The asymptotic (large-z) magnetic field structure outside the disk is obtained by solving the force-free Grad-Shafranov equation semianalytically. Jet solutions are found in which the power flow is carried mainly by the Poynting flux of the electromagnetic field and the angular momentum outflow from the disk is carried by the magnetic field. The ratio of jet luminosities (top/bottom) depends directly on the degree of asymmetry of the field and can easily be much greater than unity. It is argued that the degree of field asymmetry in the disk is determined by the asymmetry of the weak galactic field fed into the disk at large distances over long periods of time.

Wang, J. C. L.↗

Fundamentals of fluid sealing

The fundamentals of fluid sealing, including seal operating regimes, are discussed and the general fluid-flow equations for fluid sealing are developed. Seal performance parameters such as leakage and power loss are presented. Included in the discussion are the effects of geometry, surface deformations, rotation, and both laminar and turbulent flows. The concept of pressure balancing is presented, as are differences between liquid and gas sealing. Mechanisms of seal surface separation, fundamental friction and wear concepts applicable to seals, seal materials, and pressure-velocity (PV) criteria are discussed.

Zuk, J.↗

CFD Analysis of Hypersonic Flowfields With Surface Thermochemistry and Ablation

In the past forty years much progress has been made in computational methods applied to the solution of problems in spacecraft hypervelocity flow and heat transfer. Although the basic thermochemical and physical modeling techniques have changed little in this time, several orders of magnitude increase in the speed of numerically solving the Navier-Stokes and associated energy equations have been achieved. The extent to which this computational power can be applied to the design of spacecraft heat shields is dependent on the proper coupling of the external flow equations to the boundary conditions and governing equations representing the thermal protection system in-depth conduction, pyrolysis and surface ablation phenomena. A discussion of the techniques used to do this in past problems as well as the current state-of-art is provided. Specific examples, including past missions such as Galileo, together with the more recent case studies of ESA/Rosetta Sample Comet Return, Mars Pathfinder and X-33 will be discussed. Modeling assumptions, design approach and computational methods and results are presented.

Henline, W. D.↗

Analysis of an Elasto-Hydrodynamic Seal by Using the Reynolds Equation

This paper reports numerical studies of an Elasto-Hydrodynamic (EHD) seal, which is being developed for supercritical CO2 (sCO2) turbomachinery applications. Current sCO2 turbomachinery suffers from high leakage rates, which is creating a major roadblock to the full realization of sCO2 power technology. The high leakage rates not only penalize the efficiencies but also create environmental concerns due to greenhouse effects caused by the increased CO2 discharge to the atmosphere. The proposed EHD seal needs to work at elevated pressures (10–35 MPa) and temperatures (350–700 °C) with low leakage and minimal wear. The unique mechanism of the EHD seal provides a self-regulated constriction effect to restrict the flow without substantial material contact, thereby minimizing leakage and wear. This work utilizes a physics-based modeling approach. The flow through the gradually narrowing seal clearance is modeled by the well-known Reynolds equation in EHD lubrication theory, while the deformation of the seal is modeled by using the governing equations of three-dimensional solid mechanics. As for the solution methodology, COMSOL’s Thin-Film Flow and Solid Mechanics modules were employed with their powerful capabilities. The numerical results were presented and discussed. It was observed that the Reynolds equation fully coupled with the surface deformation was able to successfully capture the constriction effect. The maximum and minimum leakages were calculated to be 2.25 g/s and 0.1 g/s at P = 5.5 MPa and P = 11 MPa for the design seal, respectively. It was interesting to observe that the seal leakage followed a quadratic trend with increasing pressure differential, which can become advantageous for high-pressure applications such as sCO2 power generation technology.

42 ENGINEERING↗

Prediction of windage power loss in alternators

Simplified equations and constants, based on laminar and turbulent flow theory between parallel plates, estimate windage loss in rotating electrical machinery. Comparison of calculated results and experimental data for smooth cylindrical rotor and slotted alternator yields 7 percent maximum variation between calculated and experimental data.

Vrancik, J. E.↗

Prediction and measurement of the proportionality constant in statistical energy analysis of structures.

The fundamental equation of statistical energy analysis (SEA) states that the average power flow between two coupled vibrating systems is proportional to the difference in their average modal energies. Under certain circumstances it is possible to estimate the proportionality constant by modifying system boundary conditions on the separated systems and calculating or measuring changes in the systems. Newland's estimate, based upon blocking part of the system, is reexamined, and limitations are discussed. Three alternative methods which circumvent blocking are presented. These were applied to predict power flow in experiments on coupled beams and on coupled plates wherein power flow through the coupling was measured directly as a product of force times velocity. The measurements support the fundamental SEA relation, including the null power point where the average modal energies are equal.

Lotz, R.↗

Transport velocity transformation - A convenient method for performance analysis of multilayer solar cell structure

It is noted that in the case of low-level injection, space-charge quasi-neutrality, and spatially constant material parameters (including an electrostatic field), the individual layer can be treated analytically and the basic solar cell performance parameters can be evaluated from three equations. The first equation represents the transformation of the transport velocity across the layer from the other layer boundary. The second establishes the light-generated current output from the layer interface, under the influence of the transport velocities and minority-carrier density at both layer boundaries and of bulk recombination. The third equation describes the flow of these carriers across other layers. The power of the approach is considered to lie in its facility for analysis of the solar cell's performance layer by layer, giving a clear picture of the individual layer's influence on cell efficiency.

Wolf, M.↗