Steady-state Analytical Model Research Articles

Flooding limit in closed, two-phase flow thermosyphons

Abstract A one-dimensional, steady-state analytical model was developed to predict the CCFL in GATPTs, which treats the shear stress at the liquid-vapor interface as the sum of two terms: (a) adiabatic shear stress; and (b) dynamic shear stress. The latter accounts for the effect of evaporation/condensation at the liquid-vapor interface. The model predictions were in good agreement (within ±10%) with the data of other investigators for water and methanol. The results showed that neglecting the dynamic shear stress at intermediate and high liquid film flows underestimates the film Reynolds number at CCFL by more than 20%. The model was used to develop operation maps for R-113, acetone, methanol, heptane, water and Dowtherm-A working fluids, which give the film Reynolds number at the CCFL (or maximum power throughput) as a function of the vapor temperature in the range from 250 to 700 K. The effects of the thermosyphon inner diameter and length of the evaporator section on the film Reynolds number at CCFL were also investigated.

Analytical modeling of a self-magnetically insulated plasma focus diode

A steady-state analytical model is used to calculate the operational parameters of a coaxial-type, self-magnetically insulated ion-beam diode, called a plasma focus diode (PFD). The electrons are described by nonlaminar flow with a constant radial density distribution instead of the density profile determined self-consistently by one-dimensional laminar flow. The calculated results were compared with the experimental results obtained at the peak power, and good agreement was obtained between them. From the theoretical understanding of the PFD we obtained the scaling relations of diode impedance and the ion-current efficiency and used them to discuss the possible ways to increase the coupling efficiency and the ion-current efficiency and to reduce the instabilities in the diode operation.

Models for estimating capillary rise in a heavy clay soil with a saline shallow water table

Summary. Shallow saline water tables underlie large areas of the clay soils in the Murray basin of Australia. Accurate estimation of capillary rise is important in formulating management strategies to avoid degradation of such soils. Measured capillary rise from a saline water table was compared with capillary rise estimated by three mathematical models of varying complexity and input requirement. A quasi steady state analytical model (QSSAM), a transient state analytical model (TSAM) and a numerical model (NM) were used. An undisturbed heavy clay soil core of 0.75 m diameter and 1.4 m deep was subjected to a static saline water table at 1.2 m from the surface. A wheat crop was grown on the core and the weekly capillary rise from the water table was measured. The electrical conductivity of a I : 2 soil : water extract was determined at 0.15 m depth intervals before and 21 weeks after the introduction of the saline water table. The QSSAM did not satisfactorily estimate the initial wetting of the subsoil and the estimated capillary rise was considerably lower than the measured values. Capillary rise estimated by the TSAM was reasonably close to the measured values, but the weekly rates fluctuated considerably. The NM estimated capillary rise quite satisfactorily throughout the experiment. Except near the soil surface, the electrical conductivity values estimated by the NM were close to the measured values. For estimating total capillary rise over large areas, the TSAM is preferred over the NM because of its fewer input requirements and shorter execution time.

Natural Convection in Binary Gases Due to Horizontal Thermal and Solutal Gradients

The influence of augmenting and opposing thermal and solutal buoyancy forces on natural convection of binary gases due to horizontal temperature and concentration gradients is examined through comparison of smoke flow visualization and measured temperature and concentration distributions with numerical predictions. The observed flow at the cold wall was unsteady for opposing body forces. The same basic flow structure was observed, but the unsteady flow intensifies as the opposing solutal buoyancy force increases as compared to the thermal buoyancy force. Comparison of predicted and measured temperatures and concentrations is fair overall, but the steady-state analytical model fails to predict the unsteady flow and heat and mass transport for opposing body forces.

The dynamics of nearshore surface currents generated by tides, wind and horizontal density gradients

Nearshore surface currents measured over 23 days by HF Radar are analysed. These data are equivalent to 100 current meter deployments spaced approximately 1.5 km apart over an area 15 km square. The semidiurnal tidal constituents predominate and exhibit an even coherent propagation through the region. The higher harmonic tides are small, indicating little non-linear interaction—a consequence of the relatively deep water (20–50 m). This low level of interaction also enables the wind-driven component to be clearly separated, thereby revealing dynamics never previously identified with such clarity. The time-varying (non-tidal) residual currents are shown to be primarily due to wind forcing, with the surface currents veering up to 45° to the right of the wind at a magnitude of between 1 and 2% of the wind speed. To reproduce these features with a simple steady-state analytical model requires a vertical eddy viscosity of approximately 0.01 m 2 s −1. Using an empirical orthogonal function analysis, these wind-driven residuals are shown to move in a uniform slab-like manner with the direction rotating clockwise at a rate close to the inertial frequency (as suggested by the analytical model). The persistence of winds towards the northeast over the survey period generated significant net residual surface currents. An additional (non-wind-driven) net residual was also evident and this was shown to be consistent with forcing by (depth and time-averaged) horizontal density gradients with a vertical eddy viscosity varying linearly from 0.01 m 2 s −1 at the bed to zero at the surface. Since this eddy viscosity formulation is close to that derived for the wind-driven currents, the possibility exists of using HF Radar measurements of surface currents to determine appropriate vertical eddy viscosity coefficients for 3-D models.

Wind-driven circulation on the northern Great Barrier Reef continental shelf in summer

Observations of wind, atmospheric pressure, sea levels and current are presented for the northern (9°14′S) Great Barrier Reef continental shelf for November 1981 to May 1982. Strong low-frequency non-tidal oceanic fluctuations were observed, resulting in alternating northward and southward transport and a weak ‘mean’ circulation, and are the result of long ‘arrested’ topographic waves driven by a quasi-steady longshore wind stress and damped by turbulent bottom friction. The coefficient of friction for low-frequency currents is found to be proportional to the tidal velocities. The coefficient is also found to be much larger than that in the central (15–19°S) region of the Great Barrier Reef continental shelf, and this difference is attributed to the greatly enhanced energy dissipation by secondary circulation around coral reefs in the reef-studded northern region. Sough of Cape York (10·5°S), the primary effect of the cross-shelf wind is to complement the geostrophic set-up due to the longshore current. Intense tidal currents in the vicinity of Cape York combined with a dissipative western boundary in Torres Strait appear to prevent long wave propagation north of Cape York where a steady-state analytical model is used to show that both cross- and longshore wind components generate the reversing currents observed through Bligh Entrance.

The Prediction of Pressure Drop and CCFL Breakdown in Countercurrent Two-Phase Flow

A steady-state analytical model has been developed to predict channel pressure drop as a function of inlet vapor flow rate and applied heat flux during conditions of countercurrent two-phase flow. The interfacial constitutive relations utilized are flow structure dependent and allow for the existence of either smooth or wavy liquid films. A computer code was developed to solve the analytical model. Predictions of Δp versus vapor flow rate were found to agree favorably with experimental data from adiabatic, air/water systems. In addition, the model was used to predict countercurrent flow conditions in heated channels characteristic of a BWR/4 nuclear reactor fuel assembly.

Solar Collector Durability Evaluation by Stagnation Temperature Measurements

An analytical and experimental investigation was undertaken to evaluate an alternative method for measuring the thermal degradation of materials used in flat-plate collectors. This test method is based on measuring the temperature of the absorber under a no-flow condition before and after prolonged exposure. The primary material properties of interest are cover transmittance, solar absorptance and infrared emittance of the absorber, and thermal conductivity of insulation. The advantages and limitations of the proposed test method are compared with those for the currently used method, which is based on measuring the energy output from collectors. Experimental results from both outdoor and indoor tests are presented. Steady-state and transient analytical models are developed to evaluate the proposed test method and interpret experimental results. While the measurements required in the proposed method are simpler than those used to measure energy output, other factors, such as nonisothermal absorbers, variations in environmental conditions, and transient response, must be reconciled.

Experimental and theoretical investigation of the optogalvanic effect in the helium positive column

A linear, steady-state analytical model of the optogalvanic effect in a positive column on the 587.6-nm He transition is presented. Absolute measurements of the optogalvanic effect in a positive column on the 587.6-nm He transition are reported. The model and the experiment are found to agree over a substantial range of direct currents and over a factor of 10 in column-radius-pressure product. This model relates the absolute magnitude of the optogalvanic effect on one transition to a known ionization rate. The structure of this model should be useful in determining ionization rates of electronically excited levels from optogalvanic measurements.