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The mathematical model of vertical penetration of a steel pipe in soil with a shock pulse generator is described. The influence of the external problem parameters on the attenuation of the shock pulse propagating along the pipe is described, and the process generalities are found. The attenuation law of the mass velocity amplitude in the shock pulse along the pipe during vertical penetration in soil is revealed.

An experimental research has been carried out for vertically upward two-phase flow of air-water across inverted half U-tube bundle with or without anti-vibration bars. Pressure drop characteristics in inverted half U-tube bundle and anti-vibration bars were obtained and analyzed. New correlations for total pressure drop of two-phase flow in inverted half U-tube bundle and local pressure drop of two-phase flow in anti-vibration bars were developed. The measured two-phase pressure drops in inverted half U-tube bundle of three walls in the test sections were unequal. The pressure drop in the side wall dominated the total pressure drop of two-phase flow in inverted half U-tube bundle for 57 ≤ G −2 ·s −1 , while the pressure drop in the front wall dominated for 114 G ≤ 143 kg·m −2 ·s −1 . An obvious mass velocity effect was observed for the total pressure drop of two-phase flow in inverted half U-tube bundle. For a given Martinelli parameter, the total pressure drop of two-phase flow in inverted half U-tube bundle decreased with an increasing mass velocity. The two-phase local pressure drop data of anti-vibration bars could be fitted well in terms of the Martinelli parameter and mass velocity.

Presented are results of experimental investigation of heat transfer at downflow condensation of refrigerant R-21 in a vertical assemblage of minichannels in a plate-fin heat exchanger with plane fins. Selection of refrigerant was caused by the fact that its physical properties at room temperature are similar to those of cryogenic liquids at low temperatures. A pattern of vapor-liquid downflow in the heat exchanger channels was plotted using the working section with a transparent wall. For the mass velocity in the range of 30 to 50 kg/m2s and the wall subcooling below −2◦C, the dependence of the heat transfer coefficient on the mass vapor content is determined and a method is proposed to calculate the heat transfer coefficient that is in good agreement with the experimental data.

The performance evaluation criteria analysis for two-phase flow has been presented in this chapter. The disadvantages of using single-phase PEC correlations for two-phase flow have been discussed. Also, the factors to be considered to modify the single-phase PEC such that they can be applicable to two-phase flow have been listed.

We have regarded a mixture as a superposition of coexisting, interacting, and possibly reacting species. We have discussed the motion of monochromatic species parcels and analyzed the mixture kinematics with reference to the species diffusion velocities defined as the differences between the individual species velocities and the mixture mass velocity. In this chapter, we turn our attention to the balance of forces and introduce species and mixture stresses that develop spontaneously in hydrostatics or as a result of the motion.

In this study, a new numerical model based on the method of particles in cells, which differs in principle from the schematic of particles in Harlow cells by the fact that the particles have their own velocity and, therefore, boundaries with a vacuum are not spread, is proposed for the first time. The model makes it possible to pass the stage of the “continuous” transition to rupture development and description of the dynamics of the further state of its “banks.” Based on the Iordansky–Kogarko–van Wijngaarden mathematical model (IKW model), the formation of rupture and its further dynamics in the bubble fluid layer in the jump region of the mass velocity is numerically investigated using the proposed method. The dynamics of the state of the medium on both rupture “banks” is calculated including the structure of the rarefaction waves, fields of mass velocity and density, and cavitation development in the time range up to 2 μs when the subsequent dynamics of the layer succumbs to the prognosis.

In this study, an experimental investigation was carried out to determine the increase of pressure drop during convective condensation of R-404A vapor inside coiled wire inserted tubes. Experiments were performed for a plain tube and five coiled wire inserted tubes. Data were collected for four mass velocities. For each mass velocity, six different vapor qualities were considered. From the results, it is found that the coiled wire inserts increased the pressure drop up to 1200% compared to plain tube values. An empirical correlation is also developed to predict the pressure drop of coiled wire inserted tubes during R404-A condensation with accuracy of ±20%.

This article presents dryout results of propane in single vertical circular minichannels made of stainless steel with internal diameters of 1.70 mm and 1.224 mm. The heat flux is increased in steps up to occurrence of dryout. The effects of different parameters such as mass flux, saturation temperature, vapour quality and internal diameter on the dryout are investigated. The results show that the dryout heat flux increases with the increase in mass velocity, with the decrease of vapour quality and with the increase of internal diameter. Almost no effect of saturation temperature on dryout heat flux is observed. Generalised CHF correlations developed for macro and micro scale from the literature are also compared with the experimental results. QC 20120210

In this paper, by taking the water-water balanced counterflow heat exchanger as an example, the entransy dissipation theory is applied to optimizing the design of heat exchangers. Under certain conditions, the optimal duct aspect ratio is determined analytically. When the heat transfer area or the duct volume is fixed, analytical expressions of the optimal mass velocity and the minimal entransy dissipation rate are obtained. These results show that to reduce the irreversible dissipation in heat exchangers, the heat exchange area should be enlarged as much as possible, while the mass velocity should be reduced as low as possible.

The problem of a sphere rotating in a molecular gas is solved in the isothermal approximation. The expression for the velocity of a rarefied molecular gas entrained by a sphere rotating in it is derived for sliding flow conditions taking into account the second-order correction in the Knudsen number. A generalization of the Boltzmann kinetic equation in the BGK model to the case of rotational degrees of freedom of gas molecules is used as the basic equation. The diffusive reflection model is employed as the microscopic boundary condition on the surface of the sphere. It is shown that this approach makes it possible to take into account the dependence of the gas velocity on the Prandtl number and gas temperature.

In this paper, 325 pressure drop data points measured in return bends have been collected from the literature. The database includes 3 different fluids (R-12, R-134a and R-410A) from two laboratories. Based on this database, a new method is proposed for predicting the pressure gradient in return bends, which is the sum of the frictional pressure gradient that would be obtained in straight tubes (predicted by Muller-Steinhagen and Heck, 1986 correlation) and the singular pressure gradient (proposed equation). The proposed correlation includes only two empirical constants and exhibits the correct physical limits. Using the proposed equation, simulations have been performed to predict the effect of fluid, mass velocity and saturation temperature on the singular pressure gradient.

Solutions of the type of traveling waves defining heat transfer and gas motion with account for the relaxation of the heat flow have been obtained and investigated. A comparative analysis of solutions of both types has been carried out. It is shown that, in the case where the relaxation of the heat flow is taken into account, solutions of the type of traveling waves can exist for any relation between the velocity of the traveling wave and the velocity of sound.

The loading velocity is important in the design of packed distillation columns, and a correlation is presented for the prediction of such velocities for Raschig-ring and Berl-saddle packings. The equation is in the form: where UgL represents the loading velocity, S the specific surface of packing, F the voidage fraction, G the gas mass velocity, L the liquid mass velocity and g the gravitational constant.

A study is made of the influence of the accommodation coefficients of tangential momentum of molecules on the lower and upper plates on the behavior of the gas between moving plates with arbitrary mirror-diffuse boundary conditions. The solution is constructed in a wide range of Knudsen numbers. Expressions for the mass and heat fluxes, the friction force, and the mass velocity are obtained.

This paper describes a differential quadrature interferometer capable of measuring the mass velocities in the range of 50-10000 m/s. It can be used to obtain experimental data on the durability and kinetic properties of different classes of materials under shock-wave loading.

This paper reports results of experiments on initiation and development of detonation in cylindrical charges of a porous explosive by overdriven detonation products of a gas mixture C2H2 + 2.5 O2. Explosive charges with a bulk density of about 1 g/cm3 in fragile shells were studied. For PETN and RDX charges, the critical initial pressure of the gas mixture at which detonation initiation still occurs is determined and the pressures acting immediately on the charge are given. For PETN, critical initial pressures and initiation delays were measured for the first time for charges with particles of various diameters. The obtained dependence characterizes the following abnormal property of porous charges: there is an optimum particle size for which the explosive sensitivity is maximal. Streak records of self‐luminosity for typical initiation modes are given. Mass velocity profiles in initiation waves at different depth of the charge are obtained using an electromagnetic procedure.

A new method of calculating the critical heat flux in fuel-rod assemblies is presented. The method is based on a generalization of the experimental data in tabular form. The table for the critical heat fluxes is constructed for the correct macrocells of triangular bundles with relative rod spacing s/d=1/4 and a 9.36 mm heat diameter of a microcell for the following conditions: no effect due to peripheral zones and unheated rods; turbulizing influence of the entrance conditions and spacers; and, the heating along the length and across assemblies is uniform. To use the table for other, quite wide regions of the determining parameters, relations are presented for calculating the effect of the important parameters: heating diameter, relative rod spacing in the assembly, distance to the entrance (heated length), turbulizing influence of the spacers, and others. 1 figure, 1 table, 9 references.

The results are presented of investigations of the effect of various force factors on the level of longitudinal and transverse displacements in explosion cumulative cutting a right-angled plate. Comparison on the calculated and experimental data indicate that they are in satisfactory agreement. The results show that the level of transverse displacements is controlled by the cumulative and gas-dynamic effect of the charge whereas the level of the longitudinal mass velocity and displacements is controlled by the cumulative effect.

Experimental results on void fraction and friction pressure drop in vapour-potassium flows in the high-vapour-quality region up to unity are presented. The experimental data obtained and the pertinent results of other authors are generalized, and empirical relationship are suggested to calculate void fraction and pressure drop in two-phase liquid metal flows for channels of various configurations and orientations. The relationships are valid within the range of vapour qualities from almost zero to unit. The experimental data prove the mass velocity to have no influence on the hydrodynamic characteristics within the range of the parameters investigated. It is found in the experiments with heat supply that friction pressure losses are smaller than those for adiabatic conditions. It is shown that this result is in good correspondence with the model of the effect of injection in a boundary layer on the value of shear stresses between cases.

This paper presents a unified theory of phoretic phenomena in single-component fluids. Simple formulas are given for the phoretic velocities of small inert force-free non-Brownian particles migrating through otherwise quiescent single-component gases and liquids and animated by a gradient in the fluid's temperature (thermophoresis), pressure (barophoresis), density (pycnophoresis), or any combination thereof. The ansatz builds upon a recent paper [Phys. Rev. E 84, 046309 (2011)] concerned with slip of the fluid's mass velocity at solid surfaces--that is, with phenomena arising from violations of the classical no-slip fluid-mechanical boundary condition. Experimental and other data are cited in support of the phoretic model developed herein.

An experimental investigation of flow transient critical heat flux (CHF) for water at pressures 6.9 and 15.5 MPa is conducted under the simulation of both Boiling Water Reactor (BWR) and Pressurized Water Reactor (PWR) conditions. The influence of flow decay rates on local mass velocity and quality at CHF is explored to ensure the adequacy of local-condition approach in the CHF predictions. The assesment of transient upstream correction factor to modify the predictions of steady-state CHF correlations during the BWR flow transients are presented. A mechanistic CHF model based on the dryout of a sublayer and CHF correlations are evaluated in the predictions of PWR flow transient CHF.

Critical heat flux (CHF) of water in circular stainless steel microchannels with inner diameters ranging from ∼127μm to ∼254 μm was investigated. Forty-five CHF data points were acquired over mass velocities ranging from 1,200 kg/m2s to 53,000 kg/m2s, heated lengths from 2 cm to 8 cm, and exit qualities from −0.2 to 0.15. Most of the exit qualities fell below 0.1. It was found that CHF conditions were more dependent on mass velocity and heated length than on exit thermal condition. The results were also compared to six CHF correlations, with a mean average error ranging from 22% to 261.8%. A new correlation was proposed to better predict the critical heat flux data under the thermal-hydraulic conditions studied in this investigation. In developing the correlation, 319 data points were added from two previous studies.

Steady-State subcooled water flow boiling experiments were carried out in a uniformly heated horizontal circular channel with a 0.45-MPa exit pressure and with the mass velocity varying from 1.56 t...

Experiments were made on a critical water level under which the dryout of the heating surface occurred near the exit of the water tubes of a multitube one-through boiler. The special feature of this boiler is that the feed water rate is quite low. Based on a theoretical relation the critical water level was related to the quality, the void fraction and the slip ratio. The slip ratio was determined by the measured value of the critical water level. A correlation of the slip ratio was proposed in order to determine the water level. The correlation is expressed as a function of density ratio and Froude number, and may cover a wide range of the mass velocity including the high velocity covered in the former literatures.

In low altitude recovery, a parachute must reduce the recovery mass velocity to a predefined velocity prior to its ground impact within a height as low as possible. The article classifies various parachutes based on the parachute opening shock and distance necessary to satisfy the steady descent condition using numerical solution of experimental and theoretical relations of parachute opening and flight dynamics. Results show that the parachute filling time is the main parameter to differentiate all parachutes from each other. Based on the parachute filling time, slotted parachutes’ velocity history coverage locates between Ribbon and Ringsail parachutes whereas solid textile parachutes span a range between Extended skirt 14.3% and Guide surface parachutes. In each group decrease of parachute filling time as a result of the change in the parachute type, causes an increase in the parachute opening shock and a decrease in the parachute steady distance.

The paper presents some results of experimental and numerical studies of the late stages of the process of liquid destruction under explosive loading. The problems of relaxation of tensile stresses in a cavitation zone excited by intense rarefaction waves, and the features of the mass velocity distribution, as well as computer processing of the X-ray images of the internal structure of the opaque cavitation zone, are considered.

Shock properties of liquid argon were measured in the shock pressure up to 46 GPa by employing the two-stage light gas gun. Liquid nitrogen was used as coolant liquid. The cryogenic target system has been improved to compare with the previous work. Shock velocities were measured with self-shorting electrical probes. Impactor velocities were measured with an electrical-magnetic induction system. Mass velocities were obtained by mean of shock impedance matching method. The experimental data shows that the slope of experimental Hugoniot curve of liquid argon begins to decrease above 30 GPa.

Contact measurements of varying mass velocity and electrical conductivity in MHD channels are considered. The conditions under which the mass-velocity profile may be measured are found, and the measuring error is estimated. It is shown that MHD measurements of electrical conductivity may be made even when the mass-velocity profile is not known in advance.

The pressure drops through contractions in horizontal single and two-phase flow were investigated. A total of 167 measurements were made for four different entrance shapes to study the effects of the entrance shape on the pressure drop through a contraction in horizontal single and two-phase flow. From this data, pressure drops were calculated and compared with the pressure drops predicted by analytical models for single and two-phase flow. For single phase flow the agreement between the data and predictions is within ±25% , whereas for two-phase flow, Hoopes model which gives a better agreement than the homogeneous model, underpredicts the data as much as 45%. In addition, the effects of void fraction and liquid phase mass velocity on the pressure drop through the sudden flow channel contraction were investigated for two-phase flow.

The application of a conical fluidized bed as a remedial measure for certain inherent drawbacks of gas-solid systems is suggested. Investigations were carried out in Perspex cones with apex angles of 10°, 30°, 45° and 60°, with spherical glass beads of different sizes as the bed material, and air as the fluidizing medium. With the help of available correlations and packed bed pressure drop data, minimum fluidization velocities for the above cases were computed and compared with experimental data obtained from bed pressure drop versus fluid mass velocity plots, and the mean and standard deviations were calculated.

The systematic nature of CHF in uniformly heated vertical tubes, including the condition of very large length-to-diameter ratios, are studied by analyzing the CHF data of R-12 at 1.47 MPa, obtained as many as 1051, for tube diameter d=3, 5 and 8 mm, length-to-diameter ratio l/d=50, 100, 200, 400, 600, 800, and mass velocity G=510-6055 kg/(m2·s). It is shown that CHF data in a tube of low l/d values with mixed inlet conditions are cannot be substituted for CHF data in a tube of high l/d values with subcooled inlet conditions. Those data obtained under subcooled inlet conditions are then analyzed on the basis of two typical, existing methods for the generalized correlation of CHF, disclosing that CHF values for tubes of very small diameters tend to deviate from standard values of CHF with increasing the value of l/d. A tentative method to predict the foregoing deviation of CHF values is also given.

All loss-of-coolant-accident analysis codes solve the one-dimensional hydraulic conservation equations for a two-phase compressible fluid. Some codes allow slip between the phases, this slip being specified by a slip model. In this paper the characteristics of these conservation equations with well-known slip models (Jones, Moody, Fauske, Smith and CISE) are evaluated as a function of pressure, quality and mass velocity. Regions in which two of the characteristics are complex are shown on contour maps. The significance of these regions is discussed.

—Flame features and combustion process of fuel rich double concentric turbulent jet flames were experimentally examined. Flame appearances are very different by the velocity of the annular air jet Uam (or mass velocity ratio λ). The flames of λ = 0.25 and 0.50 for small values of Uam appear to be the conventional wrinkled laminar flames, however, for λ more than 0.74, the crowded flame appears as the result of the unburnt fuels being torn by the strong shear stress of the annular air jet and the torn–unburnt fuel crowds are intermittently ejected from the recirculation wake zone. This fact was verified by the analyses of the motion pictures and also supported by calculations of the combustion process using experimental results. Moreover, from measurements of the temperature fluctuation of the crowded flame in λ = 1.00, it was found that a comparatively high frequency fluctuation of 200∼300 Hz was superimposed on the low frequency fluctuation of 20∼50 Hz. The former corresponds with that of the mo...

An experimental investigation has been made to evaluate the friction, acceleration, and hydrostatic pressure drops in two-phase vertical crossflow across a horizontal tube bundle through the measurement of the void fraction and determination of the two-phase friction multiplier. The void fractions were found to increase with increasing mass velocity for a fixed quality level. The two-phase friction multiplier increased with increasing mass velocity for a fixed value of the Martinelli parameter in both slug and spray flow and decreased with increasing mass velocity in bubbly flows. The void fraction and two-phase friction multiplier data were correlated and used to predict with very good results the total pressure drop occurring in simulated diabatic flow tests and in actual diabatic tests using R-113.

A best-estimate prediction of transient critical heat flux (CHF) is based on instantaneous local-conditions. Eight correlations were tested against most recent blowdown heat-transfer data obtained in the U.S. The prediction results are summarized in a table in which both CISE and Biasi round-tube correlations are found to be capable of predicting the early CHF that occurs after flow reversal in the order of 1 s. The Griffith-Zuber correlation is credited for its prediction of the delay CHF that occurs in a quiescent state with slowly decaying mass velocity. A mass-velocity criterion is also suggested for its application. In many experiments, the early CHF can be closely correlated by the X  1.0 criterion; this is certainly indicative of a dryout mechanism. As for the delay CHF, a pool-boiling-type hydrodynamic crisis is suggested.

This article proposes a method of loading the medium by detonation waves with variable energy liberation in the front, and uses the method as a practical realization of the process of quasiisentropic compression. The flow in the loaded medium is calculated in the quasiacoustic approximation under the assumption that the pressure is related to the mass velocity of the material over the whole region of flow in the same way as at the shock wave front. The results indicate that using an explosive charge with variable energy liberation in the detonation wavefront as the means of loading allows an increasing pressure profile at the boundary with the given medium to be obtained. It is determined that a rising pressure profile can be obtained in a medium when it is being loaded by a detonation wave with variable energy liberation.

Diffusiophoretic separation of 0·79 μm latex spheres from nitrogen—ammonia mixtures was studied under turbulent conditions. The experiments were conducted with a small wetted wall column in which the gas mixture flowed countercurrently to a descending water film. The measured particle removal efficiencies are compared with theoretical predictions based on the hypotheses that the radial particle velocity is given by the mean molar velocity of the gas mixture, the mean mass velocity of the mixture, or Schmitt and Waldmann's (1960) expression. It is shown that the theoretical efficiencies are only functions of the molecular weights and terminal concentrations of the gaseous species and that the second hypothesis is in best agreement with experimental data. Diffusiophoresis under turbulent conditions requires large changes in gas composition to achieve even moderate particle removal efficiencies.

Axial dispersion or backmixing appears to be responsible for adverse mass velocity effects observed in trickle-flow laboratory reactors. At low Reynolds numbers typical of bench-scale units, the dispersion problem can be at least an order-of-magnitude more severe in trickle-flow than vaporphase operation. A simple perturbation criterion is derived for the minimum reactor length required for freedom from significant axial dispersion effects. It shows that the minimum length increases with both conversion and reaction order, and is inversely proportional to the Bodenstein number.

From analysis of data for the flow of steam-water mixtures in tubes at pressures between 3 MN/m2 [435 lb/in2 (abs.)] and 17·5 MN/m2 [2540 lb/in2 (abs.)] equations for friction pressure gradient are developed. These equations allow for the influence of the ‘mass velocity effect’, not previously allowed for in accepted correlations. The equations are in a form making them applicable at the critical point, and are compared with the data of Miropolskii, Isbin, and Berkowitz for steam-water flow.