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Funneling under steady-state conditions is investigated, because this problem is simple enough to be treated rigorously and provides some qualitative insights into the more difficult transient problem.
We report the EPED1 model and self-consistent core-pedestal coupling in integrated modeling are used to design the pedestal structure of the China Fusion Engineering Testing Reactor (CFETR) steady-state scenario. The key parameters, such as β p and q 95 , are based on the grassy edge-localized-mode (ELM) experimental database. In this work, we use the BOUT++ six-field two-fluid code to simulate the onset of the ELM in the CFETR steady-state scenario. The ELM size is around 0.2% in nonlinear simulations, which is in the experimental range of the grassy ELM discharges, 0.1%–1% observed in multiple tokamak devices. Linear and nonlinear simulations show that the dominant high-n ballooning modes peak around n = 40. Compared to type-I ELM crashing dynamics, grassy ELM crashing has a smaller initial crash and is then followed by three phases of turbulence spreading, which are dominated by multi-modes, a high-n mode of n = 45 and low-n mode of n = 5, respectively. In contras to type-I ELM, the perturbation of the high-n mode has a narrow width around ψ = 0.95, and magnetic island formation and reconnection occur only beyond ψ = 0.95, leading to a small initial crash. Mode–mode interaction in the multi-mode coexistence stage stops the growth of individual modes and reduces the transport of particles and heat, and these are the two reasons why the ELM size is small. In–out asymmetry of transient heat flux with a ratio of E out /E in = 3.5 is found during grassy ELM crash. The rise and delay times of the heat flux match the calculation from the free-streaming model. To evaluate the erosion of the divertor target, the energy fluence at the outer divertor target is calculated, which is 0.029 MJ m -2 , 5.5 times smaller than the tungsten melting limit 0.16 MJ m -2 . The calculated energy fluency still follows the experimental scaling law from type-I ELM experiments. The fluctuation eddies in the toroidal direction show a filament structure at the outer mid-plane. Parallel heat flux patterns with a toroidal mode number n = 10 are found at the outer divertor with an amplitude of 680 MW m -2 .
An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.
The US nuclear industry is pursuing increased cycle lengths and increasing the peak rod-averaged burnup in an effort to increase the economic viability of the US nuclear fleet. Increasing burnup will afford economic viability by enabling utilities to optimize core designs to reduce the number of fresh fuel assemblies per cycle and allow nuclear power plants to operate for a longer period of time. Longer operating periods will also decrease the number of outages experienced by a nuclear power plants and, therefore, offer utilities significant operational savings. However, extending the peak rod-averaged burnup beyond 62 GWd/tU results in operating fuel rods to higher burnup under higher power conditions. This operating regime is expected to result in higher fuel temperatures, fission gas release (FGR), and rod internal pressures (RIPs) that may challenge historical safety basis and affect high-burnup (HBU) experimental testing. In particular, these conditions directly affect fuel fragmentation, relocation, and dispersal (FFRD) susceptibility, so understanding the pretransient operating conditions is critical for developing test plans that evaluate the FFRD and develop strategies to mitigate it. This paper evaluates the operating conditions and fuel performance of HBU (greater than62 GWd/tU rod average) fuel. Additionally, it investigates fuel performance sensitivities and discusses the effect on fuel performance. Here, this work used two codes. Virtual Environment for Reactor Applications (VERA) was used to calculate steady-state power histories, identify HBU operating conditions using 10 different realistic HBU core designs, and down-select rods to a representative subset of fuel rods for subsequent BISON evaluation. The BISON fuel performance code was used to investigate steady-state HBU operating conditions and assess uncertainties associated with FGR and its effect on fuel temperatures and RIPs. The VERA and BISON results will provide direct input for HBU experimental testing and support subsequent TRACE and BISON transient fuel performance analyses.
In 1987, Grinspoon proposed that the data on hydrogen abundance, isotopic composition, and escape rate were consistent with the hypothesis that water on Venus might be in steady-state rather than monotonic decline since the dawn of time. This conclusion was partially based on a derived water lifetime against nonthermal escape of approximately 10(exp 8) years. Others have questioned this conclusion. De Bergh et al. found H2O lifetimes of greater than 10(exp 9) years. Donahue and Hodges derived H2O lifetimes of 0.4 - 5 x 10(exp 9) years. The most sophisticated analysis to date of near-IR radiation from Venus' nightside reveals a water mixing ratio of approximately 30 ppm. Recent re-analysis of Pioneer Venus Mass Spectrometer Data are consistent with a water abundance of 30 ppm. Hodges and Tinsley found an escape flux due to charge exchange with hot H(+) of 2.8 x 10(exp 7) cm(exp -2) s(exp -1). Gurwell and Yung estimated an escape flux of 3.5 x 10(exp 6) cm(exp -2) s(exp -1) from collisions with hot O produced by dissociative recombination of O2(+). Brace et al. estimated an escape flux of 5 x 10(exp 6) cm(exp -2) s(exp -1) from ion escape from the ionotail of Venus. The combined estimated escape flux from all of these processes is 3.7 x 10(exp 7) cm(exp -2) s(exp -1), suggesting a lifetime against escape for water of less than 10(exp 8) years. A recent estimate of H escape flux employing a different ionospheric model and using Pioneer Venus reentry data to estimate the response of the escape flux to the solar cycle finds a somewhat lower escape flux of 1.4 x 10(exp 7) cm(exp -2) s(exp -1), suggesting a water lifetime closer to 2 x 10(exp 8) years, significantly less than the age of the planet. Large uncertainties remain in these quantities, yet the data suggest that a source of water more recent than primordial sources is required and that a steady-state is likely. To obvious candidates for this source water are cometary impact and volcanic outgassing. Other aspects of this investigation are discussed.
A hydrodynamic model is developed for the structure of a cosmic-ray-modified termination shock. The model is based on the two-fluid equations of diffuse shock acceleration (Drury and Volk, 1981). Both the steady state structure of the shock and its interaction with outer heliospheric disturbances are considered. Under the assumption that the solar wind is decelerated by diffusing interstellar cosmic rates, it is shown that the natural state of the termination shock is a gradual deceleration and compression, followed by a discontinuous jump to a downstream state which is dominated by the pressure contribution of the cosmic rays. A representative model is calculated for the steady state which incorporates both interstellar cosmic ray mediation and diffusively accelerated anomalous ions through a proposed thermal leakage mechanism. The interaction of large-scale disturbances with the equilibrium termination shock model is shown to result in some unusual downstream structure, including transmitted shocks and cosmic-ray-modified contact discontinuities. The structure observed may be connected to the 2-kHz outer heliospheric radio emission (Cairns et al., 1992a, b). The time-dependent simulations also demonstrate that interaction with solar wind compressible turbulence (e.g., traveling interplanetary shocks, etc.) could induce the termination shock to continually fluctuate between cosmic-ray-dominated and gas-dynamic states. This fluctuation may represent a partial explanation of the galactic cosmic ray modulation effect and illustrates that the Pioneer and Voyager satellites will encounter an evolving shock whose structure and dynamic properties are strongly influence by the mediation of interstellar and anomalous cosmic rays.
A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.
Steady state and dynamic characteristics of tilting pad journal bearing in laminar and turbulent flow regime
The thermal and fast-ion transport properties of DIII-D steady-state hybrid discharges with normalized beta β N ≳ 3 are studied at low injected torque and an increased electron to ion temperature ratio T e / T i . Linear stability analysis performed with the TGLF turbulent code indicates that a high-k mode is usually dominant at smaller radii, whereas a low-k mode is usually dominant at larger radii in these plasmas. A reduction in the net injected torque from 8.6 to 4.3 N-m leads to reduced E × B shear and hence, an enhanced turbulence that was observed on the Doppler backscattering diagnostic and was also computed with TGLF. As T e / T i in the core was increased from 0.57 to 0.66 by adding electron cyclotron current drive (ECCD) to these plasmas, higher levels of transport are observed with increased high-k modes indicated by TGLF. The fast-ion transport level varied over an order of magnitude in these discharges depending on whether Alfvén eigenmodes, fishbones, or no instabilities were observed. Hybrid plasmas with fishbones have decreased fast-ion transport, compared to plasmas with Alfvén eigenmodes, since they are resonant with a smaller portion of phase space and their resonance is farther from the wall. This reduction in fast-ion transport with ECCD mitigates the increase in turbulent transport, resulting in higher performance than expected during strong electron heating. Similarly, the lowest fast-ion transport was observed in the low torque plasma, which also led to better than expected performance at this torque value. Finally, the thermal and fast-ion transport changes observed as the torque/rotation and T e / T i are varied indicate possible methods for transferring this scenario to a reactor.
We use central differences to solve the time dependent Euler equations. The schemes are all advanced using a Runge-Kutta formula in time. Near shocks, a second difference is added as an artificial viscosity. This reduces the scheme to a first order upwind scheme at shocks. The switch that is used guarantees that the scheme is locally total variation diminishing (TVD). For steady state problems it is usually advantageous to relax this condition. Then small oscillations do not activate the switches and the convergence to a steady state is improved. To sharpen the shocks, different coefficients are needed for different equations and so a matrix valued dissipation is introduced and compared with the scalar viscosity. The connection between this artificial viscosity and flux limiters is shown. Any flux limiter can be used as the basis of a shock detector for an artificial viscosity. We compare the use of the van Leer, van Albada, mimmod, superbee, and the 'average' flux limiters for this central difference scheme. For time dependent problems, we need to use a small enough time step so that the CFL was less than one even though the scheme was linearly stable for larger time steps. Using a total variation bounded (TVB) Runge-Kutta scheme yields minor improvements in the accuracy.
We use central differences to solve the time dependent Euler equations. The schemes are all advanced using a Runge-Kutta formula in time. Near shocks, a second difference is added as an artificial viscosity. This reduces the scheme to a first order upwind scheme at shocks. The switch that is used guarantees that the scheme is locally total variation diminishing (TVD). For steady state problems it is usually advantageous to relax this condition. Then small oscillations do not activate the switches and the convergence to a steady state is improved. To sharpen the shocks, different coefficients are needed for different equations and so a matrix valued dissipation is introduced and compared with the scalar viscosity. The connection between this artificial viscosity and flux limiters is shown. Any flux limiter can be used as the basis of a shock detector for an artificial viscosity. We compare the use of the van Leer, van Albada, mimmod, superbee, and the 'average' flux limiters for this central difference scheme. For time dependent problems, we need to use a small enough time step so that the CFL was less than one even though the scheme was linearly stable for larger time steps. Using a total variation bounded (TVB) Runge-Kutta scheme yields minor improvements in the accuracy.
The study of steady-state radiolysis of polyhalides is crucial as it simulates the prolonged radiation exposure that materials (e.g., alloys, molten salts) experience in reactor environments. This research provides valuable insights into the long-term effects on material properties, chemical stability, and structural integrity. It is closely linked with fundamental radiation chemistry, which aids in predicting the chemical behavior of accumulation products. Understanding the initial speciation, yield, and chemical evolution of radiolysis products is essential for managing material degradation, controlling corrosion, and ensuring reactor safety.
Steady state composition of low density nonequilibrium hydrogen plasma
Oxygen as steady state electronegative additive in cesium thermionic converter shown to improve performance without surface corrosion
Lake Erie steady state wind driven currents numerical solutions, using shallow lake model for velocity as function of depth and horizontal position
A closed-form expression for the steady-state output signal-to-noise ratio (SNR) of an n-element adaptive array excited by one desired narrow-band signal and K - 1 narrow-band jammers is obtained. This is facilitated by representing each excitation by a complex n-dimensional vector - the excitation vector. It is shown that the important system parameters are functions of scalar products of pairs of these excitation vectors. In particular, the normalized output SNR of the array is shown to be the ratio of determinants whose elements involve these scaler products. Such determinants are also shown to be involved in the expressions for the optimal array weights.
An interactive steady state frequency response computer program with graphics is documented. Single or multiple forces may be applied to the structure using a modal superposition approach to calculate response. The method can be reapplied to linear, proportionally damped structures in which the damping may be viscous or structural. The theoretical approach and program organization are described. Example problems, user instructions, and a sample interactive session are given to demonstate the program's capability in solving a variety of problems.
A comprehensive set of steady state models for spherically symmetric cooling flows in early-type galaxies is presented. It is found that a reduction of the supernova (SN) rate in ellipticals produces a decrease in the X-ray luminosity of galactic cooling flows and a steepening of the surface brightness profile. The mean X-ray temperature of the cooling flow is not affected noticeably by a change in the SN rate. The external pressure around a galaxy does not markedly change the luminosity of the gas within the galaxy but does change the mean temperature of the gas. The presence of a dark matter halo in a galaxy only changes the mean X-ray temperature slightly. The addition of a distribution of mass sinks which remove material from the general accretion flow reduces L(X) very slightly, flattens the surface brightness profile, and reduces the central surface brightness level to values close to those actually observed. A reduction in the stellar mass-loss rate only slightly reduces the X-ray luminosity of the cooling flow and flattens the surface brightness by a small amount.