Experimental and numerical studies of weak blast waves in air

Effects of viscosity and vibrational nonequilibrium on the profile of a weak, spherical N-wave in air are experimentally and numerically studied. Weak blast waves were generated, in a quiescent air dome, by spark discharges and exploding wires and observed by high frequency response microphones over 40 meters. Some similarity relationships were obtained from the blast wave experiments. For observed N-waves having less than 100 Pa peak overpressure, the peak overpressure p _f and the duration of the positive phaset _d+ are found to vary with the radial distance from the sourcer as p _f r ^–1.38 andt _d + r ^0.19, whilst the rise time of the blast wave t _f linearly increases with distance. Similar trends were also found for the negative phase of the blast wave. Numerical simulations were carried out to compare with the blast wave data. The Navier-Stokes equations for spherical symmetric flows were solved by coupling with a relaxation equation for vibrational excitation of oxygen using the random choice method (RCM) adapted to supercomputing with an operator splitting technique. The resultant N-wave profiles are in good agreement with the experimental results. The numerical results clearly indicate that the wave-easing process due to the dispersive effect of vibrational relaxation plays a dominant role in determining the rise time of the N-wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Stress-strain behavior of segmented polyurethaneureas under pure shear deformation

Elastic properties of segmented polyurethaneureas (SPUs) under pure shear deformation were investigated. Data were analyzed by using strain energy density function (W). The values of the derivatives of W with respect to the invariants of the strain tensor (I _i ; i = 1, 2, 3 ) at zero strain limit were also estimated theoretically and were compared with those estimated by experiment. The limiting value of the derivative with respect to I ₁ (W/I ₁) was shown theoretically to be 5 G/8, while the derivatives with respect to I ₂ and I ₃ (W/I ₂ and W/I ₃ were respectively-G/8 and -3G/8. The theoretical prediction could explain the asymptotic behavior of the derivatives of SPUs as well as isoprene rubber (IR) reported by Kawabata et al. at small I ₁ limit.     

Modification of Whitham's ray shock theory for analyzing the reflection of weak shock waves over small wedge angles

The weak Mach reflection phenomenon has been analyzed by applying both the shock dynamics approach and the disturbance propagation concept. The analysis which is based on modified Whitham's ray shock theory results in analytical expressions for the triple point trajectory angle,, and the shape of the curved Mach stem, which are functions of the incident shock wave Mach number,M _i, and the reflecting wedge angle, _w. The analytical results were found to be in good agreement with experimental results.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Extensional viscosity from entrance pressure drop measurements

Extensional rheological properties are important in characterization and processing of polymeric liquids. The use of entrance pressure drop to obtain extensional viscosity is particularly attractive because it can be applied to both low and high viscosity liquids using the Bagley correction obtained from a conventional capillary rheometer.Low density polyethylene of three different melt index values, including IUPAC-X (a different batch of IUPAC-A), and a high density polyethylene were tested using a commercial capillary rheometer. The entrance pressure drop (P _en ) was obtained with a zero-length orifice die with an abrupt contraction. The contraction ratio was 12:1. Predictions from several approximate analyses to calculate the uniaxial extensional viscosity _u (using an axisymmetric contraction) from P _en were compared. These comparisons are summarized in the appendices.Due to the transient nature of contraction flows, _u is also a function of the strain (). This was examined by comparing _u from P _en (Cogswell's analysis was chosen for convenience) with transient extensional viscosity ( _u ⁺) at different magnitudes of from fiber-windup technique (Padmanabhan et al., 1996). _u ⁺ at 3 was found to be close to _u from P _en (using Cogswell's analysis) for two LDPE samples that had fiber-windup data available. The magnitude of the strain in the contraction did not vary with strain rate.Dedicated to the memory of Tasos Papanastasiou     

Experimental study of boiling phenomena and heat transfer performances of FC-72 over micro-pin-finned silicon chips

Experiments were conducted to study the effects of micro-pin-fins on boiling phenomena and heat transfer from square simulated silicon chips immersed in a pool of FC-72. Two kinds of micro-pin-fins having fin thickness of 30 m and fin heights of 60 and 200 m, respectively, were fabricated on the silicon chip surface with the dry etching technique. The experiments were conducted at the liquid subcoolings of 3, 25, 35 and 45 K. The effects of dissolved air in FC-72 and chip orientation were also investigated. The boiling curve of the micro-pin-finned chips was characterized by a very small increase in wall superheat with increasing heat flux, and the wall temperatures at the CHF point for all the micro-pin-finned chips were less than the upper limit for the reliable operation of LSI chips (T_w=85°C). Liquid subcooling was very effective in elevating CHF for the micro-pin-finned chips compared to the smooth surface and other treated surfaces. The enhanced boiling heat transfer mechanisms for the micro-pin-finned chips were discussed.     

The investigation on the properties and structures of starting vortex flow past a backward-facing step by WBIV technique

An experimental investigation of a starting vortex flow around a backward-facing step was conducted in a water channel. The properties and structures of the flow were investigated by qualitative flow visualization using the hydrogen bubble method and by quantitative velocity and vorticity measurements using White-light Bubble Image Velocimetry (WBIV) — a newly developed PIV method. Some invariant properties and 4-stage structures of starting vortex flow were observed.List of symbols a flow acceleration during starting stage - h height of backward-facing step - d _v dimensionless vortex size - t time - t dimensionless time - U free uniform velocity - u, v streamwise and spanwise velocity components respectively - Re Reynolds number based on a and h - x, y streamwise and spanwise coordinates respectively in flow field - x _c , y _c dimensionless vortex center position - vorticity - ov dimensionless vorticity - _max maximum vorticity - ov _max dimensionless maximum vorticity - circulation - dimensionless circulation - kinematic viscosity This work was supported by the CNSF Grant 1939 100-1-3     

Primary and secondary bifurcation in baroclinic instability

In modelling atmospheric flows the baroclinic instability of the flow in a differentially heated rotating annulus plays a central role. This paper deals with an experimental study using LDV and flow visualization techniques. Usually the temperature difference, T, was kept fixed while the angular velocity, , was varied. On crossing the stability boundary, the primary bifurcation, the basic flow gives way to a baroclinic wave flow. For a given annulus geometry the wave number, m, of the first wave pattern was found to be uniquely defined by T. The measured critical values of , _crit, agree reasonably well with those obtained by other authors. On increasing above _crit the wave number changed, this process showing hysteresis. The situation might indicate secondary bifurcation phenomena. Flow visualization using aluminium particles shows surface flow details.This paper is dedicated to Prof. Dr. K. Gersten on the occasion of his 60th birthday     

Nonpremixed bluff-body burner flow and flame imaging study

A nonpremixed bluff-body burner flow and flame have been studied using planar flow visualization and species concentration imaging techniques. The burner consists of a central jet of CH ₄ in a cylindrical bluff-body and an outer coflowing-air stream. Planar flow visualization, using Mie scattering from seed particles added to the fuel jet, Raman scattering from CH ₄ and laser-induced fluorescence of CH combined with Raman scattering of CH ₄ provided information on turbulent flow, mixing and combustion. The CH ₄ imaging system utilized two cameras, which enhanced the dynamic range of the diagnostic system by a factor of 10 over a single-camera system. It was observed that the fuel jet stagnated on the axis due to interaction with the high velocity air flow. The flow and mixing were found to have significant coherent and noncoherent, large-scale, time-varying structures. The detailed CH ₄ Raman and CH fluorescence measurements of an air-dominated bluff-body flame revealed that the stagnation zone governs mixing and flame stability. Through large-scale mixing, the stagnated jet feeds the recirculation zone and also creates a favorable condition to stabilize the flame detached from the bluff-body. The instantaneous flame zone, as defined by CH, was found to be narrow and concentrated in an envelope around the stagnation zone. This narrow flame characteristic is consistent with that observed for jet flames. Although the internal structure of the flame envelops have not yet been defined, these results suggest that this bluff-body flame can be modeled by a flame sheet type approach, where the reaction front is captured by the large-scale structures. This should simplify the development of modeling approaches for these flows since molecular mixing and chemical reaction, which occur within the flame sheet, can be separated from the large-scale mixing process.     

Shear-induced aggregation and break up of fibril clusters close to the percolation concentration

To probe the behaviour of fibrillar assemblies of ovalbumin under oscillatory shear, close to the percolation concentration, c_p (7.5%), rheo-optical measurements and Fourier transform rheology were performed. Different results were found close to c_p (7.3%), compared to slightly further away from c_p (6.9 and 7.1%). For 6.9 and 7.1%, a decrease in complex viscosity, and a linear increase in birefringence, n, with increasing strain was observed, indicating deformation and orientation of the fibril clusters. For 7.3%, a decrease in complex viscosity was followed by an increase in complex viscosity with increasing strain, which coincided with a strong increase in n, dichroism, n, and the intensity of the normalized third harmonic (I₃/I₁). This regime was followed by a second decrease in complex viscosity, where n,n and I₃/I₁ decreased. In the first regime where the viscosity was decreasing with increasing strain, deformation and orientation of existing clusters takes place. At higher oscillatory shear, a larger deformation occurs and larger structures are formed, which is most likely aggregation of the clusters. Finally, at even higher strains, the clusters break up again. An increase in complex viscosity, n, n and I₃/I₁ was observed when a second strain sweep was performed 30 min after the first. This indicates that the shear-induced cluster formation and break up are not completely reversible, and the initial cluster size distribution is not recovered after cessation of flow.     

Identification of the Physical Parameters Used in the Thermo-Hygro-Mechanical Model

This paper describes different methods used to identify a large number of physical parameters of the thermo-hygro-mechanical coupling model. This model is developed on the basis of mechanics of porous media and deals with the prediction of response of a structure submitted to thermal, hygrometric and mechanical loading. The aim of this work is mainly to propose some experimental methods for the determination of physical parameters used previously in the model such as hygrometric parameters (liquid Biot's coefficient b _l , vapour and liquid permeability _v, _l and tangent capillary modulus N _ll). Thermal parameters such as thermal conductivity (), specific heat (C) and the thermo-hydrous expansion coefficient ( _i ^p ) have been identified using some works published previously. The different physical parameters were identified in the case of cement mortar without taking into account the influence of hysteresis.     

Interaction of a shock wave with a two-phase interface

The acceleration by an incident shock of a planar interface between a gas and a particle-gas mixture has been investigated experimentally and numerically. The experiments were conducted in a newly developed vertical shock tube in which the planar interface of the particle-gas mixture was generated and its particle concentration history was measured. Polydisperse corn starch particles with a mean diameter of 10m were used. We recorded the motion of the interface, as well as of the incident and reflected shock by using a 4 channel spark shadowgraph. The experimental conditions were Mach numberM _s=5.15 and initial pressurep ₁=50kPa for various particle concentrations in nitrogen. The reflected shock appears with a delay after the incident shock enters the particle-gas mixture. Numerical methods were employed to solve the two-phase governing equations. Experiments and numerical solutions are in good agreement.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Vorticity characteristics of the turbulent intermediate wake

Measurements of the lateral components _j (j=2 and 3) of the vorticity fluctuation vector have been made, using a vorticity probe consisting of two X-wires, in the intermediate wake of a circular cylinder. The effect of the spatial resolution of the probe on the measurement of _j has been studied. As the spatial resolution impairs, the variance and flatness factor of _j decrease whereas the skewness of _j increases. Reasonably accurate values of _j ² can be obtained by applying spectral corrections for the spatial resolution effect.Near the beginning of the intermediate wake, the variance of ₂ is larger than that of ₃ due to the significant contribution from ribs which connect consecutive spanwise roll vortices. This difference decreases with downstream distance. Also, the presence of the rolls is reflected by a local extremum in the skewness of ₃ on each side of the wake centerline. The magnitude of the extremum decreases with downstream distance.The support of the Australian Research Council is gratefully acknowledged.     

Viscoelastic properties of semidilute poly(methyl methacrylate) solutions

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G _N . Two time constants, _s and ₁, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant _k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios ₁/ _s and _k / _s were determined solely by N for each polymer species. The ratio ₁/ _s was proportional to N ^4.5 and N ^3.5 for PMMA and PS solutions, respectively. The ratio _k / _s was approximately proportional to N ^2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants _s and G _N are known.     

Determination of discrete relaxation and retardation time spectra from dynamic mechanical data

A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli,G() andG(), are converted into a discrete relaxation modulusG(t) and a discrete creep complianceJ(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data. A nonlinear regression simultaneously adjust the parametersg _i , _i ,i = 1,2, N, of the discrete spectrum to obtain a best fit ofG, G, and it was found to be essential that bothg _i and _i are freely adjustable. The number of relaxation times,N, adjusts during the iterative calculations depending on the needs for avoiding ill-posedness and for improved fit. The solution is insensitive to the choice of initial valuesg _i,0, _i,0,N ₀. The numerical program was calibrated with the gel equation which gives analytical expressions both in the time and the frequency domain. The sensitivity of the solution was tested with model data which, by definition, are free of experimental error. From the relaxation time spectrum, a corresponding discrete set of parametersJ ₀,, J _d,i and _i of the creep complianceJ(t) can then readily be calculated using the Laplace transform.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Two-color particle-imaging velocimetry using a single argon-ion laser

A swept-beam, two-color particle-imaging velocimetry (PIV) technique has been developed which utilizes a single argon-ion laser for illuminating the seed particles in a flowfield. In previous two-color PIV techniques two pulsed lasers were employed as the different-color light sources. In the present experiment the particles in a two-dimensional shear-layer flow were illuminated using arotating mirror to sweep the 488.0-nm (blue) and 514·5-nm (green) lines of the argon-ion laser through a test section. The blue- and greenparticle positions were recorded on color film with a 35-mm camera. The unique color coding eliminates the directional ambiguities associated with single-color techniques because the order in which the particle images are produced is known. Analysis of these two-color PIV images involved digitizing the exposed film to obtain the blue and green-particle image fields and processing the digitized images with velocity-displacement software. Argon-ion lasers are available in many laboratories; with the addition of a rotating mirror and a few optical components, it is possible to conduct flow-visualization experiments and make quantitative velocity measurements in many flow facilities.List of symbols d length of displacement vector - d _m distance between rotating mirror and concave mirror - n _f number of facets on rotating mirror - R seed-particle radius - v velocity in x, y plane - v _s sweep velocity of laser beams, assumed to be in y direction from top to bottom of field of view - v _x, v _y, v _z x, y, and z components of velocity - x ₁, y ₁ color-1 particle coordinates - x ₂, y ₂ color-2 particle coordinates - y _max y dimension of field of view, assumed to be the long dimension - s spatial separation of beams as they approach rotating mirror - t time separation of laser sheets or of swept beams passing fixed point - t _b time between successive sweeps through test section by same beam - t _s time required for both beams to sweep through test section - angular separation of beams reflecting from rotating mirror - fluid viscosity - v angular velocity of rotating mirror in cycles per second - seed-particle density - seed-particle response time - _v, _d, _t standard deviation of velocity, displacement, and time - vorticity This work was supported, in part, by the Aero Propulsion and Power Directorate of Wright Laboratory under Contract No. F33615-90-C-2033.     

In-line measurement of rheological properties of polymer melts

Shear viscosity (), first normal stress difference (N ₁), and extensional viscosity ( _E ) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure , N ₁, and the planar extensional viscosity ( _p ) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure and the uniaxial extensional viscosity ( _u ) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N ₁, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate _E .The hole pressure method was considered better than the exit pressure method to estimate N ₁ (due to the greater susceptibility of the latter to experimental errors). From the hole pressure method N ₁ was obtained from 100 kPa to 500 kPa over a range of shear rates from 40 s^–1 to 700 s^–1. Among the analyses used to estimate the extensional viscosity, Cogswell's is recommended due to its simpler equations without loss of much information compared to the other analyses. The range of extension rates achieved was 1 to 30 s^–1. The combination of the hole pressure and entrance pressure drop methods in a slit rheometer is a feasible design for a process rheometer, allowing the simultaneous measurement of the shear viscosity, first normal stress difference and planar extensional viscosity under processing conditions. Similarly, combining the entrance pressure drop measurements with a tube rheometer is also feasible and convenient.     

Displacement of trapped oil from water-wet reservoir rock

Displacement of oil trapped in water-wet reservoirs was analyzed using percolation theory. The critical capillary number of the CDC (Capillary Desaturation Curve) was be predicted based on the pore structure of the medium. The mobilization and stability theories proposed by Stegemeier were used to correlate oil cluster length to the capillary number needed to mobilize the trapped oil. Under the assumption that all pore chambers have the same size, a procedure was developed using the drainage capillary pressure curve and effective accessibility function to predict the CDC curve for a given medium. The prediction of critical capillary numbers was compared with the experimental data from 32 sandstone samples by Chatzis and Morrow. Also, the CDC curve of one sandstone sample was calculated using the procedure developed in this work and compared with the measured data. Very good agreements were obtained.Nomenclature a average radius of a liquid filament [m] - c constant - D pore throat diameter [m] - D _a advancing diameter of an oil cluster [m] - D _af average flowing diameter of the medium [m] - D _da controlling diameter of the medium [m] - D _r receding diameter of an oil cluster [m] - D _X difficulty index - f ratio of length to average radius of an oil cluster - F _i interfacial forces [N] - F _p force from pressure gradient [N] - g wettability function - k absolute permeability [m²] - l length of an oil cluster [m] - l _m mobile oil cluster length [m] - l _s stable oil cluster length [m] - l _w wavelength [m] - n* relative length of an oil cluster - N _c 1 capillary number defined by Equation (1) - N _c 2 capillary number defined by Equation (2) - P _b probability of oil filling a pore - P _c percolation threshold value - p _c capillary pressure [N/m²] - r radius of a pore [m] - r _e average pore radius [m] - S _n the nonwetting phase saturation - S _or residual oil saturation - S _orn normalized oil saturation - v Darcy flow rate [m/s] - X _t total fraction of pores - X _t ^a accessibility - X _e ^a effective accessibility - (D) pore throat size distribution function - _a advancing contact angle - _r receding contact angle - porosity - density of the liquid [kg/m³] - constant in Equation (4) - dynamic length of an oil cluster [m] - interfacial tension [N/m] - viscosity [N/(m s)] - p pressure gradient [N/m³]     

The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table     

Error estimates for Rayleigh scattering density and temperature measurements in premixed flames

Rayleigh scattering has become an accepted technique for the determination of total number density during the combustion process. The interpretation of the ratio of total Rayleigh scattering signal as a ratio of densities or temperatures is hampered by the changing composition through a flame, since the average Rayleigh scattering cross-section depends on the gas composition. Typical correction factors as a function of degree of reaction, fuel and equivalence ratio were calculated. The fuels considered were H₂, CH₄, C₂H₄, C₂H₆ and C₃H₈. Factors as low as 0.7 and 0.56 were found for the heaviest hydrocarbon fuel at large equivalence ratio for interpreting the Rayleigh scattering intensity as gas density and inverse temperature, respectively. This is primarily due to the presence of CO and H₂ as intermediates. As CO and H₂ are subsequently oxidized to CO₂ and H₂O, these factors approach 1.0. Conversely, the worst case, when using H₂ as a fuel, occurs in the post flame zone. However, the correction factors for H₂ are near 1.0 and the errors involved will, in general, remain within the expected experimental accuracy of a typical Rayleigh scattering system. Linear correlations of correction factors with equivalene ratio and with the product of equivalence ratio and fuel molecular weight were found and presented. The interpretation of Rayleigh scattering as temperature was found to have larger errors than the interpretation as density. Corrections for changes in gas composition were applied to Rayleigh scattering temperature measurements in the post flame region of CH₄ and C₃H₈ flames with equivalence ratios of 0.75 and 1.0. The corrected temperatures were in excellent agreement with thermocouple measurements.List of symbols A ₁, A ₂ correlation coefficients - B ₁, B ₂ correlation coefficients - C ₁, C ₂ correlation coefficients - D ₁, D ₂ correlation coefficients - C calibration constant for Rayleigh scattering optics - H total enthalpy - Î I _R /I _RO - I _i incident laser intensity - I _R Rayleigh scattering intensity - I _R0 Rayleigh scattering intensity at reference condition - N total number density of gas - N ₀ total number density of gas at reference condition - n _i index of refraction of species i - – T/T _O - T temperature - T _a adiabatic flame temperature - T ₀ reference temperature - t time - W/W ₀ - W mean molecular weight - W ₀ mean molecular weight at reference condition - W _ij rate of production of species i by reaction j - X _i mole fraction of species i - degree of reaction (T – T ₀)/(T _a – T ₀) - laser wavelength - ₀ Loschmidt number - /₀ - density - ₀ density at reference condition - dimensionless mean Rayleigh scattering cross-section - _Ri Rayleigh scattering cross-section of species i - scattering angle measured from the electromagnetic field vector - equivalence ratio     

Pressure hole errors in the annular flow measurement of the second normal stress difference

Summary For viscometric, axial, annular flow, the second normal stress differenceN ₂ is related to the difference in normal thrust across the annular space,T _rr . Past attempts using this method have yielded values ofN ₂ for polymer solutions which are different in magnitudeand opposite in sign from those obtained in other experiments. This inconsistency is attributed to errors resulting from the use of pressure holes in the measurement ofT _rr , and is supported by a second-order fluid analysis.The present work focuses on the measurement of the effect of pressure hole errors on the determination ofN ₂ with aqueous polymer solutions. In the measurement ofT _rr , simultaneous use is made of both pressure holes and miniature pressure transducers to measure and account for pressure hole errors. Results indicate that hole errors are sufficiently large to reverse the sign of the computedN ₂. This technique is therefore suggested as a preferred method for determiningN ₂, especially at high shear rates.With 6 figures