scholarly journals Modelling Surtseyan Ejecta

2021 ◽  
Author(s):  
◽  
Emma Greenbank
Keyword(s):  
Tensile Strength ◽  
Steady State ◽  
Temperature Difference ◽  
Numerical Solutions ◽  
Volcanic Eruptions ◽  
Steady State Solution ◽  
Pressure Increase ◽  
Large Temperature ◽  
Maximum Pressure ◽  
Temperature And Pressure

<p>Surtseyan ejecta are formed in shallow sub-aqueous volcanic eruptions. They occur when water, containing a slurry of previously erupted material, is washed into the volcanic vent. This slurry is incorporated into the magma and ejected from the volcano inside a ball of magma. These magma bombs containing entrained material are called, Surtseyan ejecta or Surtseyan bombs.  At the time of entrainment there is a large temperature difference between the magma (at approximately 1000°C) and the slurry (at approximately 20°C). As the inclusion temperature increases, the water contained in the slurry evaporates, causing an increase in the pressure at the boundary of the entrainment. This pressure increase is offset by the vapour diffusing through the pores of the magma. If the pressure exceeds the tensile strength of the surrounding magma the Surtseyan ejecta will rupture.  The volcanological question of interest is whether the magma ruptures. There is evidence of intact ejecta so it can be concluded that rupture does not always occur. We have developed a set of equations that transiently model the changes in temperature and pressure in Surtseyan ejecta. Numerical solutions show that the pressure rapidly increases to a stable value. Because the pressure reaches equilibrium a steady-state solution can be used to determine the maximum pressure and a criterion for rupture.</p>

scholarly journals Modelling Surtseyan Ejecta

2021 ◽  
Author(s):  
◽  
Emma Greenbank
Keyword(s):  
Tensile Strength ◽  
Steady State ◽  
Temperature Difference ◽  
Numerical Solutions ◽  
Volcanic Eruptions ◽  
Steady State Solution ◽  
Pressure Increase ◽  
Large Temperature ◽  
Maximum Pressure ◽  
Temperature And Pressure

<p>Surtseyan ejecta are formed in shallow sub-aqueous volcanic eruptions. They occur when water, containing a slurry of previously erupted material, is washed into the volcanic vent. This slurry is incorporated into the magma and ejected from the volcano inside a ball of magma. These magma bombs containing entrained material are called, Surtseyan ejecta or Surtseyan bombs.  At the time of entrainment there is a large temperature difference between the magma (at approximately 1000°C) and the slurry (at approximately 20°C). As the inclusion temperature increases, the water contained in the slurry evaporates, causing an increase in the pressure at the boundary of the entrainment. This pressure increase is offset by the vapour diffusing through the pores of the magma. If the pressure exceeds the tensile strength of the surrounding magma the Surtseyan ejecta will rupture.  The volcanological question of interest is whether the magma ruptures. There is evidence of intact ejecta so it can be concluded that rupture does not always occur. We have developed a set of equations that transiently model the changes in temperature and pressure in Surtseyan ejecta. Numerical solutions show that the pressure rapidly increases to a stable value. Because the pressure reaches equilibrium a steady-state solution can be used to determine the maximum pressure and a criterion for rupture.</p>

scholarly journals On the suitability of the Thorpe-Mason model for Calculating Sublimation of Saltating Snow

2018 ◽  
Author(s):  
Varun Sharma ◽  
Francesco Comola ◽  
Michael Lehning
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Transient Regime ◽  
State Solution ◽  
Temperature Perturbation ◽  
Alpine Regions ◽  
Drifting Snow ◽  
Tm Model

Abstract. The Thorpe and Mason (TM) model for calculating the mass lost from a sublimating snow grain is the basis of all existing small and large-scale estimates of drifting snow sublimation and the associated snow mass balance of polar and alpine regions. We revisit this model to test its validity for calculating sublimation from saltating snow grains. It is shown that numerical solutions of the unsteady mass and heat balance equations of an individual snow grain reconcile well with the steady-state solution of the TM model, albeit after a transient regime. Using large-eddy simulations (LES), it is found that the residence time of a typical saltating particle is shorter than the period of the transient regime, implying that using the steady state solution might be erroneous. For scenarios with equal air and surface temperatures, these errors range from 26 % for low-wind low-saturation conditions to 38 % for high-wind high-saturation conditions. With a small temperature perturbation of 1 K between the air and the snow surface, the errors due to the TM model are already as high as 100 % with errors increasing for larger temperature perturbations.

scholarly journals Dynamic properties of piecewise linear systems with fractional time-delay feedback

2021 ◽  
pp. 146134842110076
Author(s):  
Jianchao Zhang ◽  
Jun Wang ◽  
Jiangchuan Niu ◽  
Yufei Hu
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Analytical Solution ◽  
Goodness Of Fit ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
State Solution ◽  
Comparison Results

The forced vibration of a single-degree-of-freedom piecewise linear system containing fractional time-delay feedback was investigated. The approximate analytical solution of the system was obtained by employing an averaging method. A frequency response equation containing time delay was obtained by studying a steady-state solution. The stability conditions of the steady-state solution, the amplitude–frequency results, and the numerical solutions of the system under different time-delay parameters were compared. Comparison results indicated a favorable goodness of fit between the two parameters and revealed the correctness of the analytical solution. The effects of the time-delay and fractional parameters, piecewise stiffness, and piecewise gap on the principal resonance and bifurcation of the system were emphasized. Results showed that fractional time delay occurring in the form of equivalent linear dampness and stiffness under periodic variations in the system and influenced the vibration characteristic of the system. Moreover, piecewise stiffness and gap induced the nonlinear characteristic of the system under certain parameters.

Numerical Simulation of Thermal Stratification in the Upper Plenum of Fast Reactor

2013 ◽  
Author(s):  
Seok-Ki Choi ◽  
Tae-Ho Lee
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Thermal Stratification ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Temporal Variations ◽  
State Solution ◽  
Thermal Mixing ◽  
Commercial Code ◽  
Inlet Conditions

A numerical analysis of the thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained, and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for the steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (∼300 seconds). However, the transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A near homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates.

scholarly journals On the suitability of the Thorpe–Mason model for calculating sublimation of saltating snow

2018 ◽  
Vol 12 (11) ◽  
pp. 3499-3509 ◽  
Author(s):  
Varun Sharma ◽  
Francesco Comola ◽  
Michael Lehning
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Numerical Solutions ◽  
Steady State Solution ◽  
Transient Regime ◽  
State Solution ◽  
Alpine Regions ◽  
Drifting Snow ◽  
Tm Model ◽  
Saturation Rate

Abstract. The Thorpe and Mason (TM) model for calculating the mass lost from a sublimating snow grain is the basis of all existing small- and large-scale estimates of drifting snow sublimation and the associated snow mass balance of polar and alpine regions. We revisit this model to test its validity for calculating sublimation from saltating snow grains. It is shown that numerical solutions of the unsteady mass and heat balance equations of an individual snow grain reconcile well with the steady-state solution of the TM model, albeit after a transient regime. Using large-eddy simulations (LESs), it is found that the residence time of a typical saltating particle is shorter than the period of the transient regime, implying that using the steady-state solution might be erroneous. For scenarios with equal initial air and particle temperatures of 263.15 K, these errors range from 26 % for low-wind, low-saturation-rate conditions to 38 % for high-wind, high-saturation-rate conditions. With a small temperature difference of 1 K between the air and the snow particles, the errors due to the TM model are already as high as 100 % with errors increasing for larger temperature differences.

The Effect of Temperature Modulation on Natural Convection in a Horizontal Layer Heated From Below: High-Rayleigh-Number Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 614-620 ◽  
Author(s):  
J. Mantle ◽  
M. Kazmierczak ◽  
B. Hiawy
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Rayleigh Number ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Bottom Wall ◽  
Large Temperature ◽  
Temperature Modulation ◽  
Mean Temperature ◽  
The Mean

An experimental investigation was conducted to study the effects of wall temperature modulation in a horizontal fluid layer heated from below. A series of 45 transient experiments was performed in which the bottom wall temperature changed periodically with time in a “sawtoothlike” fashion. The amplitude of the bottom wall temperature oscillation varied from 3 to 70 percent of the enclosure’s mean temperature difference, and the period of the temperature swings ranged from 43 seconds to 93 minutes. With water as the fluid in the test cell, the flow was fully turbulent at all times. The Rayleigh number of the experiments (based on the enclosure’s height and on the mean temperature difference) was 0.4 × 108 < Ra < 1.2 × 109. It was found that for small changes in the bottom wall temperature, the cycle-averaged heat transfer through the layer was unchanged, independent of the period, and was equal in magnitude to the well-established steady-state value when the hot wall is evaluated at the mean temperature. However, this study shows that the cycle-averaged heat transfer increases notably, up to 12 percent as compared to the steady-state value, for the experiments with large temperature modulations. Futhermore, it was observed that the enchancement was a function of the amplitude and period of the oscillation.

The laminar and turbulent mixing of jets of compressible fluid. Part II The mixing of two semi-infinite streams

1957 ◽  
Vol 3 (1) ◽  
pp. 81-92 ◽  
Author(s):  
L. J. Crane
Keyword(s):  
Mach Number ◽  
Turbulent Flows ◽  
Stream Function ◽  
Temperature Difference ◽  
Numerical Solutions ◽  
Double Series ◽  
Effect Of Temperature ◽  
Large Temperature ◽  
Laminar Jet ◽  
Change Of Scale

This paper presents the application of the methods developed in a previous paper (Part I, Crane & Pack 1957) to the mixing of two parallel streams for both laminar and turbulent flows. The effects of both high velocity and large temperature difference are treated together. The method used consists in developing the stream function in a double series of powers of two parameters, the first being the Mach number and the second depending on the temperature difference of the streams. Analytical expressions are found for the terms up to the second order in the series for the stream function when the streams do not differ too greatly in velocity and temperature. However, when one of the streams is at rest the analytical method is no longer sufficiently accurate, and for this case numerical solutions are given.For laminar mixing the most important effect is that of ’change of scale’, as was found in Part I for a laminar jet at large distances from the orifice. For turbulent half-jets the effect of ’change of scale’ and the effect of the perturbation terms due to the Mach number of the flows are approximately equal and opposite, leaving the form of the velocity profile sensibly unchanged from that in incompressible flow. This last result is confirmed by comparison with some experiments of Laurence (1955) on a two-dimensional jet at M = 0·7. Lastly, the effect of temperature differences is shown to be relatively unimportant even when these are fairly considerable.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

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