Nonequilibrium stretching dynamics of dilute and entangled linear polymers in extensional flow

We propose an extension of the FENE-CR model for dilute polymer solutions [M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech. 29 (1988) 382–432] and the Rouse-CCR tube model for linear entangled polymers [A.E. Likhtman, R.S. Graham, Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation, J. Non-Newtonian Fluid Mech. 114 (2003) 1–12], to describe the nonequilibrium stretching dynamics of polymer chains in strong extensional flows. The resulting models, designed to capture the progressive changes in the average internal structure (kinked state) of the polymer chain, include an ‘effective’ maximum contour length that depends on local flow dynamics. The rheological behavior of the modified models is compared with various results already published in the literature for entangled polystyrene solutions, and for the Kramers chain model (dilute polymer solutions). It is shown that the FENE-CR model with an ‘effective’ maximum contour length is able to describe correctly the hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation also observed and computed by Doyle et al. [P.S. Doyle, E.S.G. Shaqfeh, G.H. McKinley, S.H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech. 76 (1998) 79–110] and Li and Larson [L. Li, R.G. Larson, Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow, Rheol. Acta 39 (2000) 419–427] using Brownian dynamics simulations of bead–spring model. The Rolie–Poly model with an ‘effective’ maximum contour length exhibits a less pronounced hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation.     

Simulation of ratcheting strain to a high number of cycles under biaxial loading

The Ohno–Wang kinematic hardening rule is modified to incorporate the Burlet–Cailletaud radial evanescence term for an improved simulation of the ratcheting behavior. The Delobelle parameter δ^′ is implemented in the modified model to compromise shakedown of the Burlet–Cailletaud hardening rule and over-prediction of the Ohno–Wang model. An evolution equation is proposed for δ^′ to simulate the ratcheting strain over an extended domain of cycles. Ratcheting tests were conducted on S45C steel under four types of nonproportional axial–torsional loading. The new model is found to yield reasonably accurate predictions of ratcheting strain to a much higher number of cycles compared with other studies.     

Escape of a turbulent jet under the effect of acoustic perturbations

Results are presented of experimental investigations of the local effect of acoustic oscillations of different frequency and constant intensity on the root part of a nonisothermal axisymmetric subsonic turbulent jet escaping from a gas jet atomizer at a different velocity in the S = 0.053–3.84 range of Strouhaille numbers. Data have been obtained indicating the presence of unstable escape modes of a subsonic turbulent jet in an acoustic field; experimental dependences are presented of the relative aperture of the turbulent jet flowing in an acoustic field as a function of various parameters.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 58–62, January–February, 1972.The author is grateful to A. S. Ginevskii and B. S. Burikov for discussing the results of this paper, and also to A. S. Modnov and R. A. Arkhipova for assistance in conducting and processing the experiments.     

Parametric study of the Hartmann–Sprenger tube

Experiments were conducted with a Hartmann–Sprenger tube (H–S) to study the effect of different parameters on the frequency and amplitude of acoustic fluctuations excited when the H–S underexpanded jet impinges on an in-line cavity. Time averaged shadowgraphs were acquired to study the flow field between the underexpanded jet and the cavity for varying parameters of the H–S tube. It was observed that the H–S tube primarily excited two different modes. The first mode corresponds to the jet regurgitant mode (JRG) where the frequency of oscillations scales as a function of the cavity depth. The other mode is screech where an oscillating shock is formed in front of the cavity. The screech mode excites a higher acoustic frequency than the JRG and it is observed to be a strong function of the pressure ratio R, and distance between the jet and the cavity X. At a fixed cavity length, varying standoff distance X could excite either the JRG or screech. At very low standoff distances (X/D_j<0.8), the current study indicates that there is a mode switch from screech to JRG. A cavity to jet diameter, D_c/D_j>1 was found to sustain JRG over a wide range of X. Diameter ratios D_c/D_j<1 sustained high frequency screech modes in a wide range of H–S tube parameters.     

Response of Generalized Thermoelastic Half-space with Voids to Mechanical and Thermal sources

The dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal source is investigated. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the response of various sources in the Lord–Shulman (L–S) theory and Green–Lindsay (G–L) theory for an insulated boundary and temperature gradient boundary. Some particular cases have been deduced.     

Stable nonlinear waves in a poiseuille flow

Nonlinear Tolmin-Schlichting waves are studied [1–8]. The investigation is carried out by means of a modified Stuart-Watson method [1–3]. In the case of a rigid regime of excitation terms to the fifth order are taken into account in expansions with respect to the amplitude of self-excited oscillations. The stability of self-excited oscillations with respect to two- and three-dimensional disturbances is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 40–45, September–October, 1978.The author thanks S. Ya. Gertsenshtein for attention to the work and discussion of the results.     

Calculation of the blast effect in brittle rock (fracturing by crushing,formation of cleavage cracks,and separation)

An algorithm is presented for calculating the dynamics of the development of a blast in solid, brittle fracturing rocks. The stages of the phenomenon arising and alternating in various sequences depending on the mechanical properties of the rock and power of the blast are examined in detail.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 104–120, September–October, 1970.The author thanks S. S. Grigoryan for constant attention to this study.     

Nonsteady-state plasma flows behind a moving leading front

The nonsteady-state motion of a conducting and optically transparent gas separated from a rarefied stationary medium by a front S which passes through the zone of a nonuniform magnetic field is considered. Boundary conditions at S are proposed for several interaction mechanisms of S with the rarefied medium. Solutions are obtained in linear approximation. The solutions of a general system of equations are found by means of numerical methods. The sharply nonmonotonic nature of the motion of S in the nonuniform magnetic field is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 156–162, July–August, 1973.In conclusion, the author thanks A. B. Vatazhin for useful discussions.     

Effect of magnetic field on the sedimentation of aggregate-forming weakly magnetized particles

The sedimentation model for nonmagnetic aggregate-forming particles constructed in [5] is extended to the case of weak particle magnetization. Examples are given to illustrate the analysis of certain problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 77–85, September–October, 1987.The author is deeply grateful to I. E. Tarapov, S. A. Regirer, and E. S. Losev for their interest in the work and useful discussions.     

Instability of streaky structure in a Blasius boundary layer

An experimental study was performed to analyze the stability of localized streaky structure in a Blasius boundary layer. An artificial streaky structure was created by using suction or blowing through a thin spanwise slot at the wall. The velocity gradient generated by the suction or blowing was controlled by a damper. The Reynolds number based on the displacement thickness ₁ was =280 at the slot. The behavior of the artificial streaky structure was scrutinized by damping the velocity gradient. It was found that the local streamwise and spanwise velocity gradients play a significant role in the formation of different types of instability. Artificial Tollmien–Schlichting (T–S) wave packets were created by a loudspeaker to elucidate the interaction of the streaky structure with the T–S wave packets. The T–S wave packets imposed on the streaky structure become unstable when the frequency of the T–S wave packets exceeds a certain critical frequency. The development of the T–S wave packets was investigated on the basis of the neutral stability curve.     

Stability of erythrocyte sedimentation in a constant magnetic field

The stability of erythrocyte sedimentation in the presence of a transverse component of the ponderomotive force is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 66–70, November–December, 1989.Tha author is very grateful to S. A. Regirer for his interest in the work and useful discussions.     

Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid

The hydrodynamic stability of Poiseuille flow of a viscoplastic fluid is investigated. The flow is shown to be stable for infinitesimal disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–154, November–December, 1974.In conclusion the authors thank S. A. Regirer for critical remarks.     

Flow-induced vibration of elastic slender structures in a cylinder wake

Flow-induced vibration of an elastic airfoil due to the wake propagating from an upstream cylinder at a Reynolds number of 10 000 based on cylinder diameter D was investigated. A laser vibrometer was employed to measure the bending and torsional vibration displacements at the mid-span of the airfoil and the cylinder. The dimensionless gap size S/D between the two structures was selected as the governing parameter of the flow-induced vibration problem. It is found that the vibration amplitudes of the elastic airfoil and the vortex shedding frequency of the coupled cylinder–airfoil system are strongly dependent on S/D, due to the different fluid–structure interaction experienced by the airfoil at various S/D. Strong vortex-induced vibration of the airfoil appears to be excited by the organized Karman-vortex-street (KVS) vortices in the cylinder wake for S/D>3 and becomes stabilized for S/D3. However, as a result of the shear-layer-induced vibration at an appropriate frequency, structural resonance is also found to occur even though the airfoil is located in the stabilizing range. The occurrence of structural resonance is further supported by a complementary experiment where the slender structure is an elastic flat plate. This phenomenon indicates that assuming the structures in any fluid–structure interaction problem to be rigid is not appropriate, even though they might appear to be highly stiff. The experimental results were used to validate a numerical model previously developed to estimate the structural responses in complicated fluid–structure interaction problems.     

Vorticity enhancement in convergent incompressible flows: Nonself-similar solution of the Navier-stokes equations

The enhancement of vorticity in convergent viscous incompressible flows is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 100–107, May–June, 1989.The author is grateful to S. V. Bulanov for discussion of the results and useful advice and also to Yu. K. Krasnov for discussing studies [2, 3].     

Dispersed phase motion in laminar boundary layer flow over a wedge

The motion of a dispersed phase in the laminar boundary layer on a wedge is considered with allowance for the effect of not only the Stokes force, which coincides in direction with the flow velocity, but also the transverse force (Saffman force) resulting from the transverse nonuniforrnity of the flow over the individual particle [1–3].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 34–42, November–December, 1993.In conclusion, the authors wishes to thank S. V. Manuilovich for assisting with the numerical calculations.     

A SERIES IN 1/√Re TO REPRESENT THE STROUHAL–REYNOLDS NUMBER RELATIONSHIP OF THE CYLINDER WAKE

In this Brief Note, we show that shedding frequency data is well collapsed, over a large range of Re from 50 up to at least 140,000, by using a Strouhal number that depends upon an effective wake width, which includes not only the physical body diameter, but also a characteristic width of the separating shear layers. The use of this effective wake width also leads to a new formulation for the relationship between Strouhal number (S) versus Reynolds number (Re) for the cylinder wake, which may be expressed as an expansion in powers of (1/√Re): EquationTruncated two-term or three-term series have much less error-of-fit when compared with the traditional S–Re relationships commonly in use. A good test of any S–Re functional relationship is now made possible by comparison with Henderson's numerical data for two-dimensional laminar shedding, over a much larger range of Re (up to Re=1000) than is possible to obtain experimentally. It seems significant that even a two-term fit, given by S=0·2698 −1·0271/√Re has one order of magnitude less error than the traditional three-term fit. By using such √Re-formulae in both the laminar and 3-D wake turbulent regimes, we may accurately represent S–Re data over a large range of Re, although the validity of these representations at these higher Re needs further support. In summary, this Brief Note not only provides physical support for the use of such S–Re relationships as shown above, but also demonstrates that these formulations fit the data closer than traditional S–Re expressions.     

Method of effective sections to take account of selectivity of radiation and absorption in a hot gas

A method, economical in computing time, for solving radiation transfer problems by using the integrated characteristics of the absorption spectrum, the effective sections, is elucidated. The shock layer ahead of a body around which a hypersonic gas flows is analyzed in the presence of intensive mass delivery from the surface. The machine time in the computational examples is shortened 120-fold as compared with an exact computation, and the error in calculating the radiation fluxes does not exceed 15–25%.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi FizikL, No. 5, pp. 76–83, September–October, 1972.The author is grateful to G. A. Tirskii for supervising the research and to É. S. Filippov for aid in carrying out the computations.     

Allowance for the unsteadiness of the flow in determining the critical cavitation number for marine propellers

A method of estimating the critical cavitation number for marine propeller blades is proposed. This method is based on the reduction of the three-dimensional unsteady problem to the three-dimensional steady problem and a series of two-dimensional unsteady problems.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 78–85, January–February, 1993.The authors are grateful to S. V. Kaprantsev for assisting with the experiments.     

Acoustic effect on the root part of a turbulent jet

Results are presented of experimental investigations of the effect of low-frequency acoustic perturbations of different frequency and constant intensity on the root part of a nonisothermal subsonic turbulent jet escaping from a direct-jet injector with a conical diffusor in the 0.031–0.054 range of Strouhal numbers. Experimental dependences of the mean velocity and the longitudinal intensity of the turbulence are presented as a function of different parameters for both the unperturbed flow and for the flow in the acoustic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 182–186, July–August, 1970.The authors are grateful to A. S. Ginevskii, I. M. Koshelev, and A. S. Modnov for discussing the results of this research.     

Effect of radial motion of erythrocytes on their sedimentation in a tube in an external magnetic field

The effect of the transverse component of the ponderomotive force on the aggregation and sedimentation of erythrocytes is investigated. It is assumed that the only mechanism of action of a constant magnetic field on the blood is magnetization of the erythrocytes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 120–129, September–October, 1991.The author is most grateful to S. A. Regirer for his interest in the work and useful observations.