Viscous Flow Regime Research Articles

Measurement of the Transient Glass Surface Deformation During Laser Heating

The distinct transient geometry and material response of a deforming glass surface during CO2 laser heating are related to the temperature history and the thermal regimes resulting from different energy deposition and heating rates. The transient deformation is measured using a probing system based on the photo thermal deflection technique. The variation with temperature of the optical constants yields a variable reflection signal which ultimately decreases, corresponding to a permanent volume expansion. The transient deflection signal associated with the variable deformation results from the distinct physical mechanisms in three thermal regimes, i.e., the elastic behavior, the glass transition, and the viscous flow regimes.

Viscous and Inviscid Linear/Nonlinear Calculations Versus Quasi-Three-Dimensional Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration

This paper presents a new International Standard Configuration to be added to an already existing set of 10 configurations for unsteady flow through vibrating axial-flow turbomachine cascades. This 11th configuration represents a turbine blade geometry with transonic design flow conditions with a normal shock positioned at 75 percent real chord on the suction side. Out of a set of test cases covering all relevant flow regimes two cases were selected for publication: A subsonic, attached flow case, and an off-design transonic case showing a separation bubble at 30 percent real chord on the suction side. The performed tests are shown to be repeatable and suitable for code validations of numerical models predicting flutter in viscous flows. The validity of the measured data of the two public cases was examined and comparisons with other tests were conducted. Sometimes a large difference in aerodynamic damping was observed on cases with similar flow conditions. This was investigated at three transonic cases with almost identical inlet flow conditions and only small variations in outlet Mach number. It was found that the differences in the global damping are due to very local changes on the blade surface in the shock region, which obtain a large influence by the integration because of the discrete measuring points. Hence it is recommended not to look at the global damping for code validations but more precisely to the local values. These show a common tendency, which is reproducible with different numerical methods. This was demonstrated with a potential model, a linear Euler model, a nonlinear Euler model, and a Navier–Stokes solver, all applied to predict flutter of each test case with a 2D/Q3D approach. This paper demonstrates both the limitations of inviscid codes to predict flutter in viscous flow regimes, and their cost advantage in attached flow calculations. The need for viscous code development and validation is pointed out. This should justify and encourage the publication of thoroughly measured test cases with viscous effects.

Pumping mechanism of helical grooved molecular drag pumps

The flow on a rotor of a molecular drag pump varies from viscous to slip to free molecule flow according to the decrease in pressure. As the first step, flow through a groove that is facing a wall which is moving along the groove is analyzed. The Navier–Stokes equations are simplified in the viscous and slip flow regimes and can be solved numerically with relative ease. In the free molecule flow regime, drag is caused by the momentum carried to a wall piece by gas molecules colliding with the wall piece, and the drag must be equated to the force exerted by the pressure on the two cross sections sandwiching the wall piece. A weighted linear combination of the two equations for slip and free molecule flows can illustrate the flow through the three flow regimes. The flow in ridges which leads to a leak is treated in a similar way to the flow in grooves. Then, the flows in grooves and ridges are hitherto treated separately and connected by the continuity condition of the mass flow rate normal for the groove-ridge interface. The pressure gradient which is discontinuous at the groove-ridge interface is smoothed by Boon and Tal’s “narrow groove theory” [E. F. Boon and S. E. Tal, Chemie-Ingenieur Technik 31, 202 (1959)]. The theory proposed here satisfactorily predicts the measured pumping performance throughout the three flow regimes including the transition regime from free molecule to slip flows.

Growth mechanism of hydrogenated amorphous silicon studied by in situ scanning tunneling microscopy

In situ scanning tunneling microscopy has been used to study the evolution of the surface topography of the growing surface of hydrogenated amorphous silicon (a-Si:H) in order to understand its growth mechanism. The surface is found to possess an island-like structure and the island diameter is found to increase with increasing growth temperature. A Fourier analysis of the surface roughness has an exponent of i=1.17. A comparison of the roughness of films of different thickness gives a dynamic scaling exponent of β=0.28, but the films are not particularly self-affine in character. It is argued that the exponent i is not evidence of a viscous flow regime, but that nonstochastic growth of a random network occurs, caused by a preferential hydrogen abstraction at kink-like and step-like surface sites. A simple simulation of the topography is used to support this conclusion.

Gas flow measurement by means of orifices and Venturi tubes

Numerous applications of vacuum technology require the measurement of gas throughput, as e.g. generation of calibration pressures, testing of vacuum pumps, thin film coating, and semiconductor manufacturing. Since primary methods for measuring gas flow are rather inconvenient, we have explored the gas flow measurement by means of orifices and Venturi tubes. These devices act as converters which transform a throughput to a difference pressure which can be conveniently measured. A thin orifice in the molecular flow regime and a Venturi tube in the viscous flow regime are almost fundamental converters whose characteristics can be calculated from first principles. Furthermore, these devices have high inherent stability. Thin orifices and Venturi tubes have been built and their characteristics for different gases were measured by fundamental methods. By varying diameter and inlet pressure, a wide flow range from 10 -7 to 10 5 mbar s -1 is covered. The experimental data are compared to calculated values and the characteristics are discussed.

FRICTION FACTOR IN STATIC MIXER AND DETERMINATION OF GEOMETRIC PARAMETERS OF SMX SULZER MIXERS

Pressure drops were determined in fluid flow through SMX Suizer static mixer of different sizes. In order to investigate a large range of Reynolds number, the experiments were performed with fluids of different viscosities. Pressure drops measurements in static mixer considered as a porous medium, are analysed with a capillary model for the determination of the geometric parameters of static mixers: pore diameter and tortuosity. These parameters allow the expression of pressure drops in terms of friction factor,fc as a function of pore Reynolds number, RepA universal equation is obtained for the friction factor:fc=16/Rep+,0.194 which covers both viscous and inertial flow regimes.

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) 70Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case.

Supersonic flow deceleration in plane and axisymmetric channels

Supersonic perfect gas flow in plane and axisymmetric channels with the same duct contour is studied on the basis of a numerical solution of the two-dimensional Navier-Stokes and Euler equations. The calculations were carried out at an inlet Mach number M∞=4 for various Reynolds numbers and “bell-mouth“ half-angles. The effect of these parameters, as well as that of the flow three-dimensionality, on the flow pattern is demonstrated. In particular, the existence of viscous flow regimes providing the most effective supersonic flow deceleration and a higher degree of total pressure recovery as compared with the inviscid flow is established.

The property of the vortex glass in the vicinity of the pinned vortex liquid for textured bulk YBa2Cu3O7

We have performed AC susceptibility measurement and shown the property of the vortex glass in the region near the pinned vortex liquid, where it is proposed that the velocity of flux diffusion, ν=ν0(j/jc)exp(-U/T), instead of ν=ν0exp(-U/T) in the region far away from the glass melting line for providing a gradual crossover to the viscous flux flow regime (ν ∝j, where j is current density). It is shown that the additional factor (j/j0) in the velocity is necessity to explain the experimental finding of the dependence of time scale t0 on the ac field amplitude.

Inertia as a ?safe harbour?: do fish larvae increase length growth to escape viscous drag?

Introduction Fish larvae differ from adults in their interaction with the physical environment. They hatch at a size small enough to experience water as a mainly viscous medium. Their external morphology and development are adapted accordingly (Osse and Drost, 1989). The boundary layer around the gill filaments would be too thick to allow efficient gas exchange. Only as the larvae grow bigger do the gills become functional in breathing (Osse, 1989). Viscosity also affects swimming. The flow regime around an organism depends on its size and swimming speed and can be characterized by the dimensionless Reynolds number (the ratio of inertial to viscous forces). Fish larvae hatch in the viscous flow regime and reach the inertial regime around first feeding. Experimental evidence (Vlymen, 1974) and theoretical considerations (Weihs, 1980) indicate a change of swimming style as the fish larva passes from a viscous to an inertial flow regime. The fish larva responds to the changing regime, not only by changing its swimming style, but also by adjusting its growth pattern. Fish larvae delay the gut development to keep their body flexible enough to achieve the high body wave amplitudes suitable for swimming in a more viscous regime (Osse, 1990). In spite of the obvious adjustments to the viscous flow regime, small fish larvae still experience mortality close to that of eggs (Pepin, 1991). The mortality drops drastically as the larvae grow and swimming performance improves (Bailey and Batty, 1984; Pepin, 1991). This hints at the possibility that fish larvae, instead of adapting optimally to the viscous flow regime, invest into outgrowing viscosity as quickly as possible ('safe harbour' hypothesis of Shine, 1978). To escape the viscous flow regime, a fish larva can increase its swimming speed or its size. Webb and Weihs (1986) suggest that fish larvae escape the viscous flow regime by increasing their body length. Fuiman (1983) and Osse (1990) found some indication to support this idea in the fish larvae's allometric growth patterns. This review tries to test the hypothesis that fish larvae increase their growth in length to escape the viscous flow regime. It does so by looking at the weight-length relationship of larvae from 23 species. Fish larvae should increase their growth in length until they reach the inertial flow regime at some critical length. The allometfic exponent of the weight-length relationship below this critical length should be lower

OBSERVATION OF A LINEAR REGIME IN IMAGINARY χac OF Bi-2223 SUPERCONDUCTOR

Measurements of complex AC susceptibility were performed on Bi-2223/Bi-2212 high Tc superconductor at low excitation field amplitudes. Unusual features attributable to the Bi-2223 phase are observed in the imaginary part of the AC susceptibility, χ″(T), at different excitation field amplitudes, H m . The peak temperature, T p as a function of H m defines a region in (H, T) plane, where χ″ is independent of H m . Various possible interpretations are discussed, including that of a transition to a viscous flux flow regime.

Performance of a rotating disc vacuum gauge in transitional and viscous flow regimes

The performance of a rotating disc vacuum gauge has been investigated in the transitional flow regime between molecular and viscous flow. This regime is usually described as extending from Knudsen numbers unity to approximately 0.01. A complete knowledge of the behaviour of the gauge under molecular flow conditions assists the interpretation of its behaviour and characteristic edge effects in the transitional flow regime as a combination of viscous and molecular contributions. The results suggest that the transitional regime extends from Knudsen numbers of approximately 1.0 to 0.02. The molecular-viscous intersection point is indicated to be at a Knudsen number of 0.30. The measured value of the viscosity of air at room temperature was 1.74 × 10 −5 Pa s, within 4% of the accepted value. Pressures measured utilising a semiempirical formula show limited agreement with a spinning rotor gauge in the transitional regime.

The relationship between indentation and uniaxial creep in amorphous selenium

Ultralow load indentation techniques can be used to obtain time-dependent mechanical properties, termed indentation creep, of materials. However, the comparison of indentation creep data to that obtained during conventional creep testing is difficult, mainly due to the determination of the strain rate experienced by the material during indentation. Using the power-law creep equation and the equation for Newtonian viscosity as a function of stress and strain rate, a relationship between indentation strain rate, , and the effective strain rate occurring during the indentation creep process is obtained. Indentation creep measurements on amorphous selenium in the Newtonian viscous flow regime above the glass transition temperature were obtained. The data were then used to determine that the coefficient relating indentation strain rate to the effective strain rate is equal to 0.09, or .

Gas-jet target for cluster fragmentation induced by high velocity collision

A gas-jet target for cluster fragmentation experiments has been studied in the inlet pressure range of 0.1–5.5 Torr corresponding to a target thickness range of 10 13–1.2 × 10 15 at. cm −2. The total flow has been found to be in quantitative agreement with the Poiseuille formula in the pressure range of 1.0–5.5 Torr. The profile of the jet is in good agreement with the (cos φ) 5 2 law expected in the viscous flow regime in the inlet pressure ( P 0) range of 0.1–5.5 Torr. From cross section measurements using the inlet pressure range of 1.5-5.5 Torr, the target thickness has been found to be proportional to P 0 2 as expected. The target thickness characterization has been extended in the range 10 13 to 10 14 at. cm −2 from measurements with cluster beams.

Percolation disorder in viscous and nonviscous flow through porous media.

The complete set of Navier-Stokes equations has been numerically solved for two-dimensional random pore networks subjected to site percolation disorder. Both viscous and nonviscous flow regimes have been investigated to emphasize the effect of structure and phenomenology on deviation from the classical Darcy law of permeability. It is shown that near the percolation threshold, different scaling laws apply for distinct flow conditions. At this transition region, discrepancies in the critical exponents reflect the influence of the convective momentum transfer mechanism on the overall behavior of the disordered physical system.

Gas and Mode, Vertical and Rotational Effects with a Three Piston Gauge Apparatus

A semi-automated three piston gauge apparatus has been used to measure gas species and mode effects in a low pressure pneumatic dead-weight piston gauge. Two gases, He and N2, were used in both gauge and absolute modes, as well as several "intermediate" modes, to characterize a single gauge. The results of the measurements are compared with a model for crevice effects that incorporates both molecular and viscous flow regimes. The model has previously been applied to spin decay rate measurements on the four gases He, N2, H2 and SF6, and has now been extended to account for differences in effective area arising from species changes. Mode effects remain that cannot be predicted by the model.

Experimental data and theoretical modeling of gas flows through metal capillary leaks

Metal capillary tubes are commonly used as leak elements to admit known flows of gases into vacuum systems for calibration of vacuum gaging equipment. In many instances it is desired to generate flow rates over a range of three or more decades, preferably with a single leak element. The generation of flow rates over wide ranges is possible with metal capillary leaks, but in most cases the conductance of the leak element will need to be measured as a function of the relevant pressures due to the changing of the flow regimes. Many fits to experimental data and theoretical models exist for predicting the flow rate through tubes, but their validity is not well established. In this study, measured conductances of stainless steel tubes for flow rates of 10 −8 to 10 −14 mol s −1 with several inert gases are compared with various experimental and theoretical models of gas flow in the molecular, viscous and transition flow regimes. Characteristics of crimped metal capillaries are also examined over this range of flows.

Linearization and temperature compensation up to one atmosphere for the spinning rotor gauge

While the deceleration-versus-pressure characteristic of the spinning rotor gauge (SRG) shows excellent proportionality under molecular flow conditions, strong deviations built up at the viscous flow regime. By linearization of the SRG characteristic and on-line thermal correction of the gas parameters entering the SRG pressure evaluation procedure an accuracy of 5% has been achieved for a variety of common gases under viscous flow conditions. For the thermal correction the new system comprises an ohmic temperature sensor attached to the rotor chamber. The linear pressure range of the SRG now extends from 1 μPa up to 1 atm (11 decades). Furthermore, the system is well suited for determination of the gas viscosity and its thermal increment.

Influence of planar defects on mixed state dynamics of high-T c epitaxial films

The resistive state behaviour of YBa 2Cu 3O 7 films deposited by laser ablation has been studied. The analysis of the creep and viscous flux flow regimes allowed to conclude that the one dimensional “easy slip channels”, within which vortices preferably move, play an important role. Such channels arise at planar defects (twin boundaries). Easy slip regime has been observed at temperatures above t ⩾ T/T c ⋍ 0.9 , where drastic decrease of elementary pinning force occured.

Laboratory, numerical, and oceanic fossil turbulence in rotating and stratified flows

Turbulent eddy motions are produced, and characterized, by inertial‐vortex forces. Growth of the energy, or Obukhov, scale L0 is constrained by buoyancy and Coriolis forces at the stratified fossil Ozmidov LR0 and rotational fossil Hopfinger LΩ0 length scales, and constrained at all scales by viscous, buoyancy, and Coriolis forces at sizes proportional to the stratified fossil Kolmogorov LKF and rotational fossil Kolmogorov LKƒ length scales, respectively. Universal constants of proportionality between turbulence wavelengths and these fossil turbulence length scales at their respective buoyant‐inertial, Coriolis‐inertial, buoyant‐inertial‐viscous, and Coriolis‐inertial‐viscous transitions are inferred from available laboratory, numerical, and field studies. It is important to distinguish between turbulence, which entrains, and these nonturbulent, or fossil turbulence, internal waves, Coriolis‐inertial eddies, and viscous flow regimes, which are nonlinear remnants of turbulence but do not entrain and have other properties different from turbulence. Hydrodynamic phase diagrams based on the universal constants of transition may be used to classify microstructure and mesostructure as actively turbulent, active‐fossil, fossil, or nonturbulent. One advantage of making these distinctions is to avoid undersampling errors from data sets consisting only of fossil turbulence microstructure and mesostructure. This may improve the reliability of dissipation methods used for estimating average heat, mass, and momentum fluxes in the ocean and atmosphere from microstructure and mesostructure data.