摘要:

Laminar‐to‐turbulent transition was studied experimentally in the flow of dilute, distilled water solutions of two polethyleneoxide polymers through three pipes, each 200 diam long and equipped with a ’’trigger’’ orifice, of i.d. half the pipe i.d., to provide a strong inlet disturbance. Polymer molecular weights, 0.7×106and 5.0×106, and pipe sizes, 0.292, 0.457, 0.945 cm i.d., were chosen to cause transition from the laminar regime (L) into each of three turbulent regimes associated with drag reduction,1namely, Newtonian (N), polymeric (P), and maximum drag reduction (M). The corresponding three types of laminar‐to‐turbulent transitions observed, designatedL→N,L→P,L→M, had the following characteristics: (1)L→N. In this case the transition occurred from laminar flow into a turbulent regime wherein the polymer solutions did not cause drag reduction, and the transition process appeared to be the same as in the usual Newtonian case.2,3(2)L→P. In this case the polymer solutions exhibited drag reduction at the lowest fully turbulent flow rates. The critical Reynolds number, below which turbulent slugs were not observed, was essentially the same as Newtonian. At a given Re in the transitional regime, the intermittency factor at the pipe axis was distinctly greater than Newtonian, the more so with increasing drag reducing ability of the polymer solution. The greater intermittency factor seemed to result mainly from an increased turbulent slug formation frequency relative to Newtonian; turbulent slug lengths had mean values essentially the same as Newtonian, although the dispersion about the mean was somewhat greater in the polymer solutions. (3)L→M. In this case the transition occurred from laminar flow into the turbulent regime of maximum drag reduction. Velocity fluctuations appeared at Re≃1500, appreciably lower than the Newtonian critical Re≃2000, and the fluctuation amplitude increased by an order of magnitude over the transitional range, 1500<Re<4000. Intermittency could not be discerned during this type of transition.

ISSN:0031-9171    

DOI:10.1063/1.861754

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A study of the alterations in the structure of turbulence due to the presence of PEO 301 dilute solutions was made using two experimental techniques. A photographic method was used to explore the wall region from 0.05 to 1 mm of the wall1and laser Doppler anemometry in the core and the buffer layer.2It was shown that, even if the velocities are reduced in the vicinity of the wall (in correlation with the fluid characteristics), the reduced coordinate profile remains unchanged in the laminar sublayer (y+<5). With very low concentrations (∼5 ppm) the mean velocity profile is not strongly affected even if the drag reduction is more than 40%. In the core, the shift of the profile observed by several authors was confirmed. The most important effect of the macromolecules was observed in the buffer layer where both the influence of the Reynolds number and the characteristics of the fluid were noted. The change in the structure of turbulence was observed3in measuring the streamwise turbulent intensities. It was shown that the maximum is shifted far from the wall in relation to the increase in the thickness of the viscous sublayer. A spectral analysis of the longitudinal velocity fluctuations by calculation of the probability density functions, the autocorrelation functions, and the power spectrum confirmed the idea of a transfer of energy from high frequency to low frequency turbulence structures. Therefore, it appears that the mechanism of drag reduction has to be found in the change in both the turbulent energy production (increase in the great structures) and dissipation (decrease in the importance of small eddies).

ISSN:0031-9171    

DOI:10.1063/1.861755

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The nonlinear Boltzmann equation for the relaxation to equilibrium of a homogeneous one‐component gas, is considered for a class of collision models. The models are characterized by elastic cross sections inversely proportional to the relative speed, but with arbitrary dependence on center‐of‐mass scattering angle. The Boltzmann equation is solved exactly for a particular family of physically interesting initial distributions. The distribution functions are of the similarity form and consist of the product of a Maxwell function with ’’time‐dependent temperature’’ and a linear function ofv2.

ISSN:0031-9171    

DOI:10.1063/1.861780

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The problem of impulsive spin‐up from rest of a fluid of kinematic viscosity &ngr; in a closed cylindrical container is examined numerically and experimentally. The shape of the velocity profiles is found to depend upon a parameter &agr;0=h(&ngr;/&OHgr;1/2/a2, wherehis the height, a is the radius, and &OHgr; is the angular speed of the container. When &agr;0is less than 0.005, the numerical profiles agree well with the solutions of Wedemeyer and Venezian, and the fractional spin‐up time (the time to reach some fraction of solid body rotation) is proportional toh(&ngr;/&OHgr;)−1/2. When &agr;0is larger than 1, the numerical profiles agree well with the solution of the diffusion equation, and the fractional spin‐up time is proportional toa2/&ngr;. For intermediate values of &agr;0, the numerical profiles agree well with experiment, and the dependence of the fractional spin‐up time on &OHgr;, &ngr;,h, andavaries with &agr;0, with radial positionr, and with the dimensionless angular velocityW=v/r&OHgr;, wherevis the azimuthal velocity.

ISSN:0031-9171    

DOI:10.1063/1.861781

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

The Burgers equationut+uux=&ngr;uxxrepresents pure inertial motion except for the effects of viscosity &ngr;. If &ngr;=0, this equation becomes u˙=0 and describes the inertial motion of a one‐dimensional continuum until the time of formation of discontinuities, or ’’shocks’’. The study of pure inertial motion is extended to an arbitrary number of dimensions. Starting from some initial state of motion each parcel of the continuum may or may not have the intrinsic ability to form a shock, this property being a function of the symmetrical part of the velocity gradient matrix in the vicinity of the parcel. This study determines the conditions for which a parcel will, in fact, form a shock, the time that is required, and the temporal development of the full velocity gradient matrix and of coordinate invariants of the flow such as the divergence and the vorticity.

ISSN:0031-9171    

DOI:10.1063/1.861782

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A method is presented to determine the steady, three‐dimensional, potential flow (neglecting surface tension) of a slender stream of fluid in the presence of gravity. Three basic flows are considered: jet flow (for which the bounding surface is entirely free); pipe flow (for which the bounding surface is entirely specified) and channel flow (for which the bounding surface is partially free and partially specified). The leading terms in the asymptotic expansions of these flows, which are called outer expansions, are presented. The leading terms in the pressure distribution for each of the three basic flows are also computed and several examples are presented.

ISSN:0031-9171    

DOI:10.1063/1.861783

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

Higher order terms in the outer asymptotic expansions for flows of slender streams in the presence of gravity are computed. In particular, for the case of jet flow, higher order terms corresponding to a basic flow with either a circular or elliptical cross‐sectional shape are discussed in detail and an inherent spatial instability (due to the effects of gravity) in the jet is discussed. Higher order terms for pipe flow and channel flow are also calculated and an example is presented. The pressure distribution within the flow is also computed and the effects of the pressure on the flow when a free surface is present is discussed.

ISSN:0031-9171    

DOI:10.1063/1.861784

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

A systematic method is presented, in some detail, for solving Navier–Stokes turbulence problems. This method is based on the use of a three‐point (or triple) Green’s functionG(3). A new set of covariant turbulence equations is thereby derived from the Navier–Stokes equation, without having to make anyadhocassumptions; in fact, these equations simply constitute the first order terms of an expansion in a new ordering parameterR. The derived set of equations preserve Galilean invariance, and reduce to the direct‐interaction approximation when certain definite terms are arbitrarily disregarded. It is the omission of these terms which is primarily responsible for the loss of Galilean invariance in several previous approximations. It is shown that random Galilean invariance is closely associated with a dependence of ⟨G(3)⟩ on the correlation length of the turbulence. A simple approximation is suggested which expresses ⟨G(3)⟩ in terms of a new (modified) single Green’s function. The modified Green’s function is random Galilean invariant, but does not involve an arbitrary constant as does the Green’s function used in the test‐field model.

ISSN:0031-9171    

DOI:10.1063/1.861785

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

Time and spatially resolved studies have been made of imploding shock waves in a 20 cm hemispherical chamber filled with 2H2+O2mixtures at high initial pressures (7–56 atm). Implosion pulse durations and maximum temperatures were found to be (10–4) &mgr;sec and (4500–6000) K, respectively. Peak pressure for a 7 atm initial pressure experiment was estimated to be (12.5±1.0) ×103atm. The focus of the imploding shock was examined by using an image converter camera in both streak and framing modes. No major instabilities or symmetry defects were noted. The results may be of interest for laser fusion applications.

ISSN:0031-9171    

DOI:10.1063/1.861786

出版商:AIP    

年代:1977

数据来源: AIP

摘要:

An asymptotic theory is formulated to describe the effects of surface electron emission on the behavior of a stationary, collision‐dominated, weakly ionized gas in the vicinity of a spherical probe. Limits where an electron energy balance yields either constant or variable electron temperatures are examined. When the microscopic emission current is of the order of the product of the plasma random current and the small normalized sheath thickness associated with no emission and isothermal electrons, the theory, under certain restrictions, follows the corresponding no‐emission formalism; the results, however, are different due to the altered surface boundary conditions. In particular, moderate emission can suppress the saturation behavior usually exhibited by the current‐voltage characteristics at highly negative probe potentials. When the microscopic emission current is of the order of the plasma random current itself, even the overall structure of the flow field may exhibit significant variations. In the cold ion limit, at a given level of massive emission, the nonisothermal theory predicts a saturation of the electron current at highly negative probe potentials due to the divergence of the quasi‐neutral potential drop, whereas the isothermal theory does not. When the ion and electron temperatures are of the same order of magnitude, the potential drop across the sheath becomes comparable to that across the quasi‐neutral region.

ISSN:0031-9171    

DOI:10.1063/1.861787

出版商:AIP    

年代:1977

数据来源: AIP