Quasi-steady Regime Research Articles

Laser plasma interaction studies in the context of shock ignition—Transition from collisional to collisionless absorption

The shock ignition concept implies laser pulse intensities higher than 1015 W/cm2 (at the wavelength of 351 nm), which is the commonly accepted limit where the inverse bremsstruhlung absorption dominates. The transition from collisional to collisionless absorption in laser plasma interactions at higher intensities is studied in the present paper with the help of large scale one-dimensional particle-in-cell simulations. The initial parameters are defined by the hydrodynamic simulations corresponding to recent experiments. The simulations predict that a quasi-steady regime of laser plasma interaction is attained where the total laser energy absorption stays on the level of ∼65% in the laser intensity range 1015–1016 W/cm2. However, the relation between the collisional and collisionless processes changes significantly. This is manifested in the energy spectrum of electrons transporting the absorbed laser energy and in the spectrum of the reflected laser light.

Impact of maximum borehole depths on inverted temperature histories in borehole paleoclimatology

Abstract. A quantitative assessment is presented for the impact of the maximum depth of a temperature-depth profile on the estimate of the climatic transient and the resultant ground surface temperature (GST) reconstruction used in borehole paleoclimatology. The depth of the profile is important because the downwelling climatic signal must be separated from the quasi-steady state thermal regime established by the energy in the Earth's interior. This component of the signal is estimated as a linear increase in temperature with depth from the lower section of a borehole temperature profile, which is assumed to be unperturbed by recent changes in climate at the surface. The validity of this assumption is dependent on both the subsurface thermophysical properties and the character of the downwelling climatic signal. Such uncertainties can significantly impact the determination of the quasi-steady state thermal regime, and consequently the magnitude of the temperature anomaly interpreted as a climatic signal. The quantitative effects and uncertainties that arise from the analysis of temperature-depth profiles of different depths are presented. Results demonstrate that widely different GST histories can be derived from a single temperature profile truncated at different depths. Borehole temperature measurements approaching 500–600 m depths are shown to provide the most robust GST reconstructions spanning 500 to 1000 yr BP. It is further shown that the bias introduced by a temperature profile of depths shallower than 500–600 m remains even if the time span of the reconstruction target is shortened.

Thermoelectric instability induced by single pulses and alternating currents in second-generation superconducting tapes

We have studied current flow instabilities in a second-generation superconducting tapes and the transition of the tapes into the resistive state. Contrary to the usual quasisteady instability regimes, here we consider the adiabatic case in which the sample is heated rapidly. Two kinds of measurements of the current-voltage characteristics (CVC) have been made, specifically, with excitation of the tape by a single sinusoidal current pulse I (t)=I0sin(ωt) at different amplitudes I0 and by a continuous ac current. The main results were obtained for current amplitudes I0 exceeding the critical current Ic. We find that the dynamic CVC are essentially reversible for low amplitudes, whereas they become irreversible and acquire an N-shape for higher current amplitudes. The dynamic CVC change radically if the dissipated energy attains a threshold value Wth roughly equal to 5mJ∕cm for our tapes. When this energy is reached, the tape undergoes a transition to the resistive state owing to formation of normal domains. The development of the instability with steady ac currents was studied at relatively small amplitudes such that the energy dissipated per half cycle is much lower than Wth. Even in this case, a tape undergoes a transition to the resistive state because of energy accumulation (heat pumping). With this pumping, the transition takes place after a definite number of ac cycles, when the total accumulated energy reaches the same threshold value Wth. The specific features of the dynamic CVC are interpreted qualitatively, with the appearance of resistive domains taken into account. Estimates based on the CVC agree well with our experimental data. These results can be useful in the design of superconducting fault current limiters.

Isogeometric analysis of free-surface flow

This paper presents the first application of isogeometric analysis, a new computational technology built on higher-order and higher-continuity basis functions employed in Computer-Aided Design and computer graphics, to the computation of free-surface phenomena described using the level set approach. The method is based on the variational framework that is suitable for discretization by standard finite elements as well as the basis functions employed in isogeometric analysis. The underlying numerical formulation globally conserves mass and preserves a sharp air–water interface for the entire length of the simulation. The numerical tests indicate that the proposed methodology gives an accurate description of the free-surface behavior in both quasi-steady and dynamic regimes. Furthermore, very good per-degree-of-freedom accuracy is obtained when higher-order and higher-continuity isogeometric discretizations are employed in free-surface computations.

Numerical investigation of heat and mass transfer of an evaporating sessile drop on a horizontal surface

A convection-diffusion model is developed to analyze the effect of buoyant convection in the surrounding air on the heat and mass transfer phenomena during the evaporation of a pinned water drop deposited on a horizontal substrate of large dimensions. The substrate is maintained at constant temperature which can be equal or higher than the temperature of the ambient air. The mathematical model accounts for the motion of the gas phase surrounding the drop due to thermal and solutal buoyancy effects, while only thermal diffusion is considered in the liquid phase. A quasisteady state regime is adopted because of the slow motion of the liquid-gas interface as well as the induced heat and mass transfer phenomena in both phases. The numerical results obtained with the diffusion model or the convection-diffusion model show that heat and mass transfer rates are important toward the contact line. The heat required for evaporation process is taken from the environment, both the liquid and the gas phase, and results in a small cold zone on both sides of the interface. The influence of the buoyancy in air is of greater importance in the lower part of the interface and beyond a distance of a contact radius above the droplet. A weak variation of the evaporation rate is observed on a wider range of contact angle for high wall temperatures. The diffusion model underestimates the overall evaporation rate by 8.5% for a wall temperature equal to an ambient temperature of 25 °C and by 27.3% for a wall temperature of 70 °C. Numerical calculations show that the length of the heated wall has very little effect on the evaporation process when it exceeds 25 times the contact radius.

Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory

Nanoelectromechanical oscillators are very attractive as sensing devices because of their low power requirements and high resolution, especially at low pressures. While many experimental studies of such systems are available in the literature, a fundamental theoretical understanding over the entire range of operating conditions is lacking. In this article, we use our newly developed Bhatnagar–Gross–Krook based low Mach number direct simulation Monte Carlo method to study the noncontinuum drag force acting on a cylinder oscillating normal to a wall. We explore quasisteady flows in which ωτf⪡1 as well as unsteady flows for which ωτf=O(1). Here ω is the oscillation frequency and τf is the characteristic time for the development of the gas flow. The drag force per unit length acting on a long cylindrical wire is studied as a function of the Knudsen number, defined in terms of the mean free path λ and the radius of the cylinder R as Kn=λ/R. For quasisteady flows, we also present theoretical calculations for the slip regime, Kn⪡1, and the free molecular flow regime, Kn⪢1. Simulations of unsteady gas flow around a sinusoidally oscillating cylinder near a wall indicate that the drag force per unit length nondimensionalized by 4πμU approaches constant values for ωτf⪡1 (quasisteady flow) and for ωτf⪢1. Here μ is the gas viscosity and U is the maximum value of the nanowire velocity. The simulation results are compared with experimental measurements in the quasisteady regime.

Stability of liquid sheet edges

Accelerating edges of thin liquid sheets are ubiquitous and are known to experience a longitudinal (along-the-edge) instability, which often leads to their break-up and atomization. The fundamental physical mechanisms of this instability are studied analytically in the quasisteady regime, which admits a concise modeling. It is discovered that the classical Rayleigh–Taylor mechanism is substantially modified which leads to a stability picture different from that for flat interfaces, in part due to an interplay with Rayleigh–Plateau mechanisms. In particular, as the Bond number increases, first, only one critical wavenumber is excited, but for higher values of the Bond number several critical wavenumbers can coexist with the same growth rates. This allows for the transition from the regular picture, in which one wavelength sets the pattern, to the frustrated picture, in which a few wavenumbers compete with each other.

Combustion response of an aluminum droplet burning in air

The combustion in air of a 100 μm-diameter aluminum droplet is studied by direct Navier–Stokes simulations. The model only considers the gas phase and includes a reduced Al/O 2 kinetic scheme with 8 species and 10 reactions. The model is validated against experimental burn time data and appears to be fairly correct despite its simplicity. The unsteady combustion is then investigated by superimposing an acoustic disturbance to the mean flow. The velocity-coupled response is computed for different frequencies and slip Reynolds numbers. A resonance peak is found to occur when the acoustic time scale matches the gas diffusion time scale. For lower frequencies however (typically below a few kHz), a quasi-steady regime seems to hold out which means that assuming quasi-steady combustion (e.g., given by a D 2 model) is valid in this case. In this regime, the computed response corresponds with a theoretical expression obtained by a linearization of the Ranz–Marshall correction term. This implies that unsteady aluminum combustion is strongly dependent on convection effects.

Diffusion in the general theory of relativity

The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space avoids difficulties in the general relativistic stochastic calculus. The general relativistic Kramers equation in the phase space is derived both in the parametrization of phase-space proper time and the coordinate time. The transformation of the obtained diffusion equation under hypersurface-preserving coordinate transformations is analyzed and diffusion in the expanding universe is studied. It is shown that the validity of the fluctuation-dissipation theorem ensures that in the quasisteady state regime, the result of the derived diffusion equation is consistent with the kinetic theory in thermodynamic equilibrium.

The role of shock–flame interactions on flame acceleration in an obstacle laden channel

Flame acceleration was investigated in an obstructed, square-cross-section channel. Flame acceleration was promoted by an array of top and bottom surface mounted obstacles that were distributed along the entire channel length at an equal spacing corresponding to one channel height. This work is based on a previous investigation of the effects of blockage ratio on the early stage of flame acceleration. This study is focused on the later stage of flame acceleration when compression waves, and eventually a shock wave, form ahead of the flame. The objective of the study is to investigate the effect of obstacle blockage on the rate of flame acceleration and on the final quasi-steady flame-tip velocity. Schlieren photography was used to track the development of the shock–flame complex. It was determined that the interaction between the flame front and the reflected shock waves produced from contact of the lead shock wave with the channel top, channel bottom, and obstacle surfaces govern the late stage of flame acceleration process. The shock–flame interactions produce oscillations in the flame-tip velocity similar to that observed in the early stage of flame acceleration, but only much larger in magnitude. Eventually the flame achieves a globally quasi-steady velocity. For the lowest blockage obstacles, the velocity approaches the speed of sound of the combustion products. The final quasi-steady flame velocity was lower in tests with the higher obstacle blockage. In the quasi-steady propagation regime with the lowest blockage obstacles, burning pockets of gas extended only a few obstacles back from the flame-tip, whereas burning pockets were observed further back in tests with the higher obstacle blockage.

Measurement and modeling of pulsatile flow in microchannel

An experimental study of pulsatile flow in microchannel is reported in this paper. Such a study is important because time-varying flows are frequently encountered in microdevices. The hydraulic diameter of the microchannel is 144 μm and deionized water is the working fluid. The pressure drop across the microchannel as a function of time is recorded, from which the average and r.m.s. pressure drops are obtained. The experiments have been performed in the quasi-steady flow regime for a wide range of flow rate, frequency of pulsations, and duty cycle. The results suggest that the pressure with pulsations lies between the minimum and maximum steady state pressure values. The average pressure drop with pulsation is approximately linear with respect to the flow rate. The theoretical expression for pressure has also been derived wherever possible and the experimental data is found to lie below the corresponding theoretical values. The difference with respect to the theoretical value increases with an increase in frequency and a decrease in flow rate, with a maximum difference of 32.7%. This is attributed to the small size of the microchannel. An increase in frequency of square waveform leads to a larger reduction in pressure drop as compared to rectangular waveform, irrespective of the duty cycle. The results can be interpreted with the help of a first-order model proposed here; the model results are found to compare well against the experimental results. A correlation for friction factor in terms of the other non-dimensional governing parameters is also proposed. Experimental study of mass-driven pulsatile flow in microchannel is being conducted for the first time at these scales and the results are of both fundamental and practical importance.

Elastic-backscatter-lidar-based characterization of the convective boundary layer and investigation of related statistics

Abstract. We applied a ground-based vertically-pointing aerosol lidar to investigate the evolution of the instantaneous atmospheric boundary layer depth, its growth rate, associated entrainment processes, and turbulence characteristics. We used lidar measurements with range resolution of 3 m and time resolution of up to 0.033 s obtained in the course of a sunny day (26 June 2004) over an urban valley (central Stuttgart, 48°47' N, 9°12' E, 240 m above sea level). The lidar system uses a wavelength of 1064 nm and has a power-aperture product of 2.1 W m2. Three techniques are examined for determining the instantaneous convective boundary layer (CBL) depth from the high-resolution lidar measurements: the logarithm gradient method, the inflection point method, and the Haar wavelet transform method. The Haar wavelet-based approach is found to be the most robust technique for the automated detection of the CBL depth. Two different regimes of the CBL are discussed in detail: a quasi-stationary CBL in the afternoon and a CBL with rapid growth during morning transition in the presence of dust layers atop. Two different growth rates were found: 3–5 m/min for the growing CBL in the morning and 0.5–2 m/min during the quasi-steady regime. The mean entrainment zone thickness for the quasi-steady CBL was found to be ~75 m while the CBL top during the entire day varied between 0.7 km and 2.3 km. A fast Fourier-transform-based spectral analysis of the instantaneous CBL depth time series gave a spectral exponent value of 1.50±0.04, confirming non-stationary CBL behavior in the morning while for the other regime a value of 1.00±0.06 was obtained indicating a quasi-stationary state of the CBL. Assuming that the spatio-temporal variation of the particle backscatter cross-section of the aerosols in the scattering volume is due to number density fluctuations (negligible hygroscopic growth), the particle backscatter coefficient profiles can be used to investigate boundary layer turbulence since the aerosols act as tracers. We demonstrate that with our lidar measurements, vertical profiles of variance, skewness, and kurtosis of the fluctuations of the particle backscatter coefficient can be determined. The variance spectra at different altitudes inside the quasi-steady CBL showed an f−5/3 dependency. The integral scale varied from 40 to 90 s (depending on height), which was significantly larger than the temporal resolution of the lidar data. Thus, the major part of the inertial subrange was detected and turbulent fluctuations could be resolved. For the quasi-stationary case, negative values of skewness were found inside the CBL while positive values were observed in the entrainment zone near the top of the CBL. For the case of the rapidly growing CBL, the skewness profile showed both positive and negative values even inside the CBL.

Investigations on Quasi-Steady Characteristics for an Airfoil Oscillating at Low Reduced Frequencies

Wind tunnel experiments were conducted on NACA-0015 airfoil model to investigate the effect of the reduced frequency (κ=0.0001to 0.5) and that Reynolds number (Re=0.2E06to 0.7E06) on the aerodynamic characteristics and hysteresis behavior associated with the oscillating motion of the airfoil. Pressure measurements were conducted on the midspan of the airfoil for quantitative results. Although dynamic stall study has been conducted to greater extent of reduced frequencies, for current work, emphasis is made on investigating the low reduced frequency regimes up to which the steady conditions prevail under dynamic mode of operation. In present investigations of oscillating sinusoidalα=10∘+15∘sin(ωt)motion, the airfoil was allowed to execute oscillating motion from static to almost steady (quasi-steady) conditions with the incremental increase in the reduced frequency. The limiting conditions ofκandRefor quasi-steady state are carefully extracted and analyzed. Static and quasi-steady conditions are critically assessed in context of the existence of laminar separation bubble within the optedReregime. The flow separation was found to be trailing edge flow separation with existence of LSB upstream towards the leading edge with no evidence of unsteady flow reversals. Normal force defect and pitch damping factor are estimated for varied range ofReandκwithin the quasi-steady conditions. Re effect is dominant at steady and quasi-steady regimes while the effect of reduced frequency is negligible in this domain. Minor hysteresis effect associated with the stalling and reattachment point is due to existence of weak stall flutter which is further restrained by the oscillatory motion of the airfoil. Laminar separation bubble traced during steady condition is conserved in quasi-steady domain as well.

Mechanism of Structure-Driven Nonlinear Instability of Double Tearing Mode in Reversed Magnetic Shear Plasmas

The trigger for the nonlinear destabilization of the double tearing mode (DTM), referred to as a structure-driven instability leading to explosive growth and subsequent collapse, is investigated. We use the reduced MHD equations that solve the evolution of perturbations from an equilibrium deformed by two-dimensional magnetic islands during the slow evolution of the quasi-steady nonlinear regime. By examining conditions near marginal stability (under which the explosive growth is not triggered), we have identified a new secondary instability that starts growing when the magnetic energy of the primary fluctuations associated with the islands reaches a critical level. The energy source of this instability is different from that of the linear DTM; it originates in the spatial deformation due to the DTM-driven magnetic islands and is responsible for the subsequent nonlinear destabilization. The growth rate of this secondary instability is found to be proportional to the magnetic energy, suggesting that it exhibits modulational characteristics.

Steady and unsteady Görtler boundary-layer instability on concave wall

The subject of the present combined experimental and theoretical investigation is the steady and unsteady linear Görtler instability. The majority of previous experiments were devoted to the steady Görtler vortices, despite the unsteady ones are also observed in real transitional flows. Moreover, even for the steady Görtler vortices no quantitative agreement between the experimental and theoretical linear-stability characteristics was obtained, especially for disturbance amplification rates. The experimental difficulties were connected, in particular, with a rather poor accuracy of measurements at zero disturbance frequency, a possible influence of nonlinearity, and an admixture of non-modal (transient) growth mechanism. All these difficulties have been overcome in the experimental part of the present study by means of: ( i) tuning-out of the exact zero frequency of Görtler vortices and working, instead, with quasi-steady perturbations of very low frequencies, ( ii) performing measurements at low disturbance amplitudes, and ( iii) minimization and careful estimation of the disturbance-source near-field by means of utilizing a special controlled disturbance source and performing special numerical computations for exact experimental conditions. A detailed study of all linear-stability characteristics for essentially unsteady Görtler vortices was performed in this paper as well. The results are obtained in a range of Görtler numbers 13 ≲ Gö ≲ 17.3, frequency parameters F = 0.56–22.70, and spanwise wavelength parameters Λ = 149–775 (close to the most amplified Görtler modes). Appropriate calculations based on locally-parallel and non-local non-parallel linear-stability theories were performed and compared quantitatively with experimentally obtained linear-stability characteristics. For the first time all stability characteristics measured for steady Görtler vortices (in quasi-steady regimes) are found to agree very well with those calculated for the most amplified first discrete-spectrum mode of the linear Görtler-instability problem. Similar good agreement is obtained for essentially unsteady Görtler vortices. The roles of effects of the base-flow non-parallelism and the disturbance-source near-field are examined.

Structure of numerically simulated katabatic and anabatic flows along steep slopes

Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is derived and quantitatively verified against the DNS data.

Ten proofs of the generalized second law

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing previous research, this review offers new perspectives, and strategies for overcoming limitations of the existing proofs. A long introductory section addresses some choices that must be made in any formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should one use the global or the apparent horizon? Is it necessary to assume any entropy bounds? If the area has quantum fluctuations, should the GSL apply to the average area? The definition and implications of the classical, hydrodynamic, semiclassical and full quantum gravity regimes are also discussed. A lack of agreement regarding how to define the quasi-stationary regime is addressed by distinguishing it from the quasi-steady regime.

Effect of Mach number on transonic flow past a circular cylinder

The effect of Mach number on transonic flow past a circular cylinder is investigated numerically for the free-stream Mach number M ∞ from 0.85 to 0.98 and the Reynolds number 2×105 based on the diameter of the cylinder. The work provides an insight into several salient features, including unsteady and quasi-steady flow state, formation of local supersonic zone, and evolution of turbulent shear layer. Results show that there exist two flow states dependent of a critical Mach number M cr around 0.9. One is an unsteady flow state characterized by moving shock waves interacting with the turbulent flow in the near region of the cylinder for M ∞<M cr, and the other is a quasi-steady flow state with nearly stationary shock waves formed in the near wake for M ∞>M cr, suppressing vortex shedding from the cylinder. Some flow behaviors in the unsteady and quasi-steady flow states are revealed. From time evolution of flow structures, local supersonic zones are identified in the wake and generated by two typical processes, i.e. reverse flow behind the cylinder and shed vortices in the near wake. The convective Mach number M c of turbulent shear layers shed from the cylinder is identified nearly as M c<1 in the unsteady flow regime and M c>1 in the quasi-steady flow regime, resulting in different evolutions of the shear layers.

Turbulence and waves in numerically simulated slope flows

Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is proposed and quantitatively verified against the DNS data.

Magnetron sputtering of YBaCuO target: Effects of discharge voltage and deposition rate variation

The time variations of the discharge voltage and YBaCuO film deposition rate in an on-axis magnetron sputterer are studied. In the case of an YBaCuO ceramic target, the discharge voltage and the rate of superconducting phase deposition decrease with time, exponentially approaching a quasi-steady regime. At a pressure of 100 Pa, a decrease in the magnetic field induction near the target from 1200 to 600 G leads to a rise in the discharge voltage by 25–30% and increases the deposition rate more than twofold. The deposited films offer high electrophysical parameters, as demonstrated with a high-frequency circuit: the intrinsic Q factor of the circuit at 64.5 MHz is found to be 2.7 × 105.