Wave Number Density Research Articles

Phenomenological model of disturbance waves in annular two-phase flow

A new, phenomenological, model of disturbance waves in annular two-phase flow is presented. The model builds upon the three-field (gas, drops and film) one-dimensional model of annular two-phase flow by considering the disturbance waves as an additional fluid field, traveling over a thin liquid base film, along with its own mass, momentum and energy conservation equations. The waves are modeled as fluid particles characterized by basic macroscopic parameters such as the wave shape factor (amplitude/width) and the wave number density (spatial frequency of waves). Phase change is considered and relevant closure models are developed for the field mass and momentum exchange rates (drop entrainment/deposition and waves/base film interactions). A Boltzmann transport equation of wave number density is introduced to model the hydrodynamic non-equilibrium effects related to the wave creation, merging and splitting processes, characteristic of developing annular two-phase flows (due to e.g., inlet effect, phase change, geometrical change or transient). Finally, the base film mass and wave number density sink and source rates are modeled using a relaxation time approximation. The new model is motivated and fully documented in this paper and has been implemented in the latest version of the transient sub-channel analysis code MEFISTO-T. While the proposed model framework is generic for coherent disturbance waves, the required wave characteristic correlations are specifically developed and calibrated using high pressure steam/water experiments under equilibrium conditions relevant of Boiling Water Reactor operation. The model relaxation times are then estimated by comparing the model predictions against measured wave parameters downstream various flow perturbations (evaporation and film suction), along the channel recovery length toward equilibrium. For all considered experiments, the model predicts the averaged wave and base film parameters typically within +/-20% and is able to capture the axial development of disturbance wave characteristics. The consideration of non-equilibrium effects is found fundamental to the accurate simulation of axially developing annular two-phase flows.

Increase of turbulence and transport with resonant magnetic perturbations in ELM-suppressed plasmas on DIII-D

Long-wavelength turbulence increases dramatically in the outer regions of DIII-D plasmas with the application of resonant magnetic field perturbations (RMPs) that suppress edge-localized modes (ELMs). Correspondingly, transport increases and global energy confinement decreases in these low-collisionality RMP-ELM suppressed discharges. The core and pedestal density are sharply reduced, while ion and electron temperatures may change only slightly. Low wavenumber density turbulence (k⊥ρi < 1) in the range of 60–300 kHz, measured with beam emission spectroscopy, is modified and generally increases throughout the outer region (0.6 < ρ < 1.0) of the plasma in response to RMPs over a range of q95 values; ELM suppression, in contrast, occurs for a narrower range in q95. Radial magnetic field modulation experiments indicate that these turbulence modifications occur on a time scale of a few milliseconds or less near ρ = 0.85–0.95, significantly faster than transport time-scales and faster than the local pressure gradients and shearing rates evolve at these locations. As the internal coil current is modulated in a square-wave fashion from 3.2 to 4.2 kA, the turbulence magnitude varies in phase by 30% or more, while local density changes by only a few per cent. This dynamical behaviour suggests that the turbulence is directly affected by the RMP, which may partially or largely explain the resulting increased transport and stabilization of the pedestal against peeling–ballooning instabilities that are thought to drive ELMs.

Quasioptical design of integrated Doppler backscattering and correlation electron cyclotron emission systems on the DIII-D tokamak

The quasioptical design of a new integrated Doppler backscattering (DBS) and correlation electron cyclotron emission (CECE) system is presented. The design provides for simultaneous measurements of intermediate wavenumber density and long wavelength electron temperature turbulence behavior. The Doppler backscattering technique is sensitive to plasma turbulence flow and has been utilized to determine radial electric field, geodesic acoustic modes, zonal flows, and intermediate scale (k∼1-6 cm(-1)) density turbulence. The correlation ECE system measures a second turbulent field, electron temperature fluctuations, and is sensitive to long poloidal wavelength (k≤1.8 cm(-1)). The integrated system utilizes a newly installed in-vessel focusing mirror that produces a beam waist diameter of 3.5-5 cm in the plasma depending on the frequency. A single antenna (i.e., monostatic operation) is used for both launch and receive. The DBS wavenumber is selected via an adjustable launch angle and variable probing frequency. Due to the unique system design both positive and negative wavenumbers can be obtained, with a range of low to intermediate wavenumbers possible (approximately -3 to 10 cm(-1)). A unique feature of the design is the ability to place the DBS and CECE measurements at the same radial and poloidal locations allowing for cross correlation studies (e.g., measurement of nT cross-phase).

High Wavenumber Density Fluctuation Measurement in the HT-7 Tokamak

A three channel CO2 laser forward scattering diagnostic system was set up to study the core plasma density fluctuation in the HT-7 tokamak. The range of the wavenumber measurement in the poloidal direction was kθ = 12 cm−1 to 34 cm−1 and the wavenumber resolution was Δk = 2.5 cm−1. The wavenumber spectrum, the coexisting modes and the micro-instability eruption in experiments are presented.

Observation of reduced core electron temperature fluctuations and intermediate wavenumber density fluctuations in H-mode plasmas

In this paper, we report observations of reduced core electron temperature and intermediate-scale density fluctuations in H-mode. Electron temperature fluctuation levels are observed to decrease from L-mode levels ( for kθρs < 0.5 as measured by correlation electron cyclotron emission radiometry) by at least a factor of four in H- and quiescent H-mode regimes in the DIII-D tokamak (r/a = 0.7). Linear stability calculations (using the trapped gyro-Landau fluid (TGLF) code) indicate that the observed temperature fluctuations are associated with L-mode ITG turbulence which is shear-stabilized at the L- to H-mode transition. Recent results from DIII-D provide the first experimental evidence that, in addition, intermediate-scale turbulence (0.5 < kθρs ⩽ 3) is reduced at the L–H transition. A 30–40% prompt reduction (r/a ⩾ 0.7) has been found at the L–H transition in co-injected medium density plasmas, with a larger decrease (⩾75%) observed near the pedestal top. Experimental results and TGLF calculations indicate that intermediate/small scale turbulence persists in H-mode at a reduced amplitude (0.6 ⩽ r/a ⩽ 1) and may substantially contribute to the residual anomalous H-mode electron heat transport.

Detection of zonal flow spectra in DIII-D by a dual-channel Doppler backscattering system

Doppler backscattering (DBS) has been successfully used to measure the E x B flow velocity and local intermediate wavenumber density fluctuation levels in the DIII-D tokamak. Depending on the launch angle and the frequency of the probing beam, the signal backscattered from the plasma cut-off layer is sensitive to density fluctuations at a specific perpendicular wavenumber (1 < or = k(perpendicular rho(s)) < or = 4). Due to the localization and high time resolution for poloidal flow measurements, DBS is well suited to detect stationary and time-dependent shear flows [zonal flows (ZFs)]. We present a novel scheme to measure ZF spectra using a dual-channel DBS system capable of simultaneously probing two minor radii separated by a distance of 0.2 cm < Delta r < 3 cm. Frequency spectra of geodesic acoustic modes and low frequency ZFs (f or = 10 kHz) have been obtained for 0.6 < r/a < 0.95.

Experimental characterization of coherent, radially-sheared zonal flows in the DIII-D tokamak

The application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas, has provided temporally and spatially resolved measurements of the turbulence flow-field. Features that are characteristic of self-generated zonal flows are observed in the radial region 0.85⩽r/a⩽1.0. These features include a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m=0, narrow radial extent (krρI&amp;lt;0.2), and whose frequency varies monotonically with the local temperature. The approximate effective shearing rate, dvθ/dr, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence, and the density fluctuation amplitude is modulated at the frequency of the observed flow oscillation. Some phase coherence is observed between the higher wavenumber density fluctuations and low frequency poloidal flow fluctuations, suggesting a Reynolds stress contribution. These characteristics are consistent with predicted features of zonal flows, specifically identified as geodesic acoustic modes, observed in 3-D Braginskii simulations of core/edge turbulence.