Dr. Y. Shtemler
RESUME
OF SOME SCIENTIFIC WORKS AND INDUSTRIAL PROJECTS
Bubble-to-dispersed-bubble regime transition under downward filtration [1]
On the macro (bed) scale the model describes filtration of a weakly compressible liquid with micro-bubbles through fixed beds formed by spherical particles. The bubble diameter is assumed to grow up to the diameter of the capillary throat. To further simplify the problem we use the smallness of the ratio of the throat to the mean diameter of capillaries (for regular packing this value equals approximately 0.2). The state equation for bubble liquids is derived via homogenization of an ensemble of spherical bubbles in the liquid (cell model). According to the developed model the bubble-regime transition occurs when the bubbles, growing due to the downflow pressure drop, block capillary throats. Since the micro (pore) scale peculiarities of the system are accounted for only through the mean diameter of capillaries, the model loses its physical meaning when the bubbles block the capillary throats and break up into smaller bubbles. The critical parameters of the model determining such micro-scale instability agree with the experimental data for bubble-to-dispersed-bubble regime transition.
Two-stage model for liquid atomization in convergent-divergent nozzles [2]
According to experimental data primary atomization of liquid into coarse drops occurs immediately at the exit from the liquid delivery tube within the atomizing nozzle; further coarse-drop break up into finer droplets takes place within a relaxation zone down the flow. The proposed two-stage model describes these transitions as primary and secondary atomization shocks. The mixture behind the primary atomization shock is described in the phase-insulated limit, while the mixture behind the secondary atomization interface is assumed fine enough to be in a homogeneous equilibrium state. The model predictions agree with experimental results and can be used to optimize the atomizer geometry and operating conditions.
Hydraulic model for double-nozzle vortex chamber [3]
The double-nozzle vortex chamber comprises tangential peripheral inlet slits and two coaxial central outlets for fluid discharge: a conventional nozzle for axial outflow and an auxiliary internal nozzle for radial outflow through the perforated lateral surface. Such a device can be used for dusty fluid purification, for control of flow rate through the conventional nozzle, etc. A multi-zone approach to flow modeling enables the main design parameters and operating conditions to be estimated. In each zone, the flow is described by the inviscid flow equations. The solutions obtained do not satisfy any matching condition at the neighboring zone interfaces, however, they are related by integral conservation laws for mass, momentum and energy, by the hydraulic principle of maximum flow rate, and by the boundary conditions at the chamber walls. The model provides an estimation of the necessary perforated area for a given pressure differential between the conventional and auxiliary nozzles.
Bubble oscillations at near-to-critical gas state [4]
Real-gas bubble oscillations in a viscous compressible liquid were simulated for a near-to-critical gas state typical of industrial chemical reactors. The analysis uses the Chapman-Plesset approach, but employs a linearized real gas constitutive equation whose coefficients are obtained from experimental data on sound speeds and specific heat capacities. The system is considered in a near-to-critical region, but outside the immediate vicinity of the critical state. This means that the real gas properties should be taken into account, though the singularity of thermodynamic parameters is not yet manifested. It is shown that the near-to-critical state dissipation decrement and natural frequency of a bubble are much higher than under the normal conditions.
Rayleigh-Taylor instability [5, 6]
The Rayleigh-Taylor instability was investigated for an inviscid incompressible fluid without surface tension. At large times, such instability appears in the form of alternating unsteady narrowing elongated spikes falling with constant acceleration, and wide steady-state bubbles rising with constant velocity. To eliminate the steady-state interface singularity in the spikes, the interface was treated as a sum of a known asymptotic expansion singular at the spike vertex and an unknown regular part represented by a Fourier series. Only the unbounded main term of asymptotic expansion is usually eliminated. We showed, however, that although the next expansion term vanishes at the singular point, it should not be dropped since this leads to unphysical oscillations of the solution. The second asymptotic term is known up to a coefficient undetermined within the steady-state formulation. Its unique value that yields a non-oscillating solution may be found from conservation laws for the unsteady problem in the long time limit. It also follows from the conservation laws that spikes acceleration is equal to buoyancy acceleration. However, the steady-state problem contains the bubble velocity as a parameter and has a solution for a range of these velocity values. The unique physically correct value of bubble velocity is determined by the smoothness condition for the curvature of the bubble surface at its vertex. It may be noted that in a closely related problem on horizontal gravity currents the unique solution is fully determined by conservation laws.
Buoyancy effects in premixed flames propagating through channels [7, 8]
In the limit of strong thermal expansion of the burned gas, an analogy was explored between the steady state propagating flames and the gravity currents in horizontal channels or Rayleigh-Taylor instability in vertical channels. The principal distinction between flames and purely hydrodynamic systems concerns their behavior near the channel walls. While hydrodynamic systems exhibit infinitely long spikes, the flame interfaces develop into long but finite narrow skirts determined by combustion effects. Experiments show that these skirts are well approximated by linear correlations. We showed that the hydrodynamic solution for the bubble in an outer region can be matched asymptotically with a linear flame skirt in the inner region; the matching determines the skirt slope to the channel wall [7]. Such an approach enabled us to simplify the problem by eliminating the perturbed vortex flow problem for the burnt gases behind the flame front. The results obtained are in quantitative agreement with available experimental data for lean mixture burning.
Effective dynamic hardness for projectile penetration [9]
Knowledge of the effective dynamic hardness of armor is required for numerical and analytical studies of the penetration process. The method developed for the effective dynamic hardness estimation is based on a dimensional analysis of experimental data on impact crater depth for small metallic projectiles penetrating metallic targets. We found that, being scaled by the value of the effective dynamic hardness, these data are described (in dimensionless variables) by a single master curve. This curve and the crater depth measurements are employed to identify the effective dynamic hardness values.
Ultrasonic welding [10]
A mathematical model for evaluating the ultrasonic welding bond strength of two materials takes into account spot fusion weldments, where only one of the contacting materials melts and the thickness of the melting zone is comparable with the roughness of the contacting surfaces. Material debonding occurs along the interface between the asperities of one of the welded materials and the melting zone of the other material. Thus, the strength is assumed to be limited by wetting of rough contact surfaces. This allows cumbersome calculations of residual stresses to be avoided, and the ultimate strength to be estimated explicitly. Numerical simulation demonstrated fair agreement with the available experimental data. A qualitative explanation was obtained for the seemingly abnormal behavior of the bond strength of ultrasonic welding that varies non-monotonically with the increase of the load applied.
Couette flow between free-to-move cylinders in a self-gravitation field [11
Stability was studied of the central coaxial system of two cylinders which are free to move in the radial direction. This system is employed for the instability study of a planet in the vicinity of its equator that is modeled as a fluid confined between the cylindrical solid shell and kernel in a self-gravitation field. Among various predicted unstable modes there exists also a purely hydrodynamic unstable mode caused by free radial motion of the cylinders. This mode can cause instability in the conventional Couette flow between rotating cylinders due to a weak beat of the cylinder axes.
Transient instability of Stokes flows [12]
We studied the linear stability of the following 1D self-similar solutions to Navier-Stokes equations (Stokes flows expanding with time): boundary layer, jet, wake, and shear layer. To avoid limitations inherent in the conventional approach that freezes the inhomogeneous variables, the slow-time approximation is applied to stability study of the Stokes flows. They were shown to be stable asymptotically at large times, but time inhomogeneity of the Stokes flows can lead to transient instability during a finite time.
Stable subcritical oscillations in boundary layers and channels [13, 14]
The weakly nonlinear stability was studied for a wide class of viscous flows: boundary and shear layers, jets, wakes, and channel flows. We showed that subcritical stable self-sustained oscillations exist in the Poiseuille-Couette flow and Blasius boundary layer, while in the free flows (shear layers jets and wakes) supercritical oscillations are possible. In particular, the bifurcation hypothesis, valid asymptotically near the transition of the excitation-of-oscillations regime, put forward for Poiseuille flow by Arnold (Geometrical methods in the theory of ordinary differential equations, Arnold V.I., N.Y., Springer-Verlag, 1983, 334p.) has been confirmed by numerical simulations [13].
Origin,absorption&dispersion of noises in towed underwater acoustic systems (Project for Defense Industry[15])
Towed underwater acoustic devices detect acoustic signals from a remote source with the use of microphones equally spaced within an oil-filled shell with yield walls. In some practical cases measurements reveal broadband noises with no external source of sound at an angle to the axis of the underwater acoustic system with no dependence on rope length or velocity of the towed system and on the towing velocity. The noises may be misinterpreted as signals from a real distant source of sound. An explanation is given for the noise origin, the angle value and the boundaries of the frequency band are estimated by a boundary layer approximation for long-wave oscillations of a thin oil-filled elastic axisymmetric shell in water.
Heat transfer and hydrodynamics of wet stack (Project for Israel Electric Corp. [16])
The Project was prepared for the Israel Electric Corporation planning the construction of a new power plant with wet purification of exhaust gases. Participation in the expert evaluation and discussion of proposals was envisaged within its framework. The processes going on in a real stack were analyzed to describe their possible scenarios and determine the main factors responsible for them, to order them by the size of their contributions to droplet emission from the stack and to formulate the ensuing requirements to the stack constructors. The possibility for reliable mathematical modeling of particular processes was also evaluated. The general description is given of the geometry of the wet stack and of the main physical processes in its sections (duct, stack proper and choke) together with formulation of the main specifications for the test stack. A detailed dimensional analysis is given for various physical processes in the stack proper.
Clearing of a passage through a minefield (Project for Defense Industry [17])
Clearing of a passage through a minefield after explosion of a line charge is studied. Mine displacements caused by the effects of the air shock waves are studied which overcome mine-soil friction . While other less dangerous cases of mine movements: jumps, flight etc. are ignored. The clearance width is estimated based on the mine energy balance, dimensional analysis and statistic treatment of experimental data on mine displacements against mine-soil friction. Being dimensionalized by the characteristic values of the effective friction coefficient, of the power of the line charge, etc., these data are described by a single master curve depending on the other parameters, such as mine volume, shape and others. This curve and the clearance width measurements allow to identify the effective friction coefficient. The secondary employment of the approach with a known effective friction coefficient enables the power of the line charge to be predicted which is necessary for the required value of the clearance width.
Nonlinear Galerkin Method [18]
An approach was proposed to introduce principles of the asymptotic method of strained coordinates into the
traditional Galerkin procedure to solve differential equations. It uses conventional expansions for unknown solutions
in the Fourier series, but in parametric form. Moreover, independent variables are also represented by the Fourier
series. The unknown coefficients of the truncated Fourier series are determined by the minimum of equation discrepancy.
The proposed approach was tested by model partial differential equations.
References
1. Shtemler Y., Shreiber I.R., Herskowitz M., Gelman E.,
Bubbly liquid filtration
through fixed beds , Orpheus 2000, 5-th Jubilee workshop on: Transport
Phenomena in Two-Phase Flow, Pamporovo, Bulgaria, 55-62, 2000.
&
Micro-scale instabilityof bubbly flows in packed beds, The
4-th Intern. Confer. on Multi Phase Flows,USA,New Orlean, 2001
2. Shtemler Y., M.P. Levitsky, I.R. Shreiber, S.P. Levitsky and Y. Berkovich,
Two-stage atomization model for liquid jet disintegration in gas atomizers,
Applied Mechanics and Engineering, 5(4),821-842, 2000.
3. Shtemler Y ., Levitsky M.P. , Hydraulic theory for double-nozzle vortex chamber,
Orpheus 2000, 5-th Jubilee workshop on: Transport Phenomena in Two-Phase
Flow, Pamporovo, Bulgaria, 7-12, 2000.
4. Shreiber I.R., Shtemler Y., Herskowitz M., Levitsky S., On bubble oscillations at
near-critical gas state, Proceedings of the Second International Simposium on
Two-Phase Flow Modelling and Experimentation, Pisa, 2, 1003-1007, 1999.
5. Shtemler Y., Sivashinsky G., Chernyavski V.,
Evolution of Unsteady Jets in the Rayleigh-Taylor Instability,
Nonlinear Processes in Geophysics, 5, 181-186, 1998.
6. Chernyavsky V., Shtemler Y., The nonlinear asymptotic stage of the
Rayleigh-Taylor instability with wide bubbles and narrowing spikes,
in: Geophysical Monograph 83, IUUG, 18, 97-102, 1994.
7. Shtemler Y., Sivashinsky G., On flame propagation through a horizontal channel,
Comb. Science and Technol., 119, 35-50, 1996.
8. Shtemler Y., Sivashinsky G., On upward propagating flames,
Comb. Science and Technol., 102, 81-93, 1994.
9. Pridor A., Slepyan L., Ayzenberg M., Shtemler Y., Modelling Diverse Engineering
Aspects of Penetration. 27 Israel Conference on Mechanical Engineering, Haifa,
172-174, 1998.
10. Drozdov A., Shtemler Y., Evaluation of bond strength at ultrasonic welding,
26 Israel Conference on Mechanical Engineering, Haifa, 383-385, 1994.
11. Chernyavskij, V.M.; Shtemler, Yu.M. Stability of Couette flow between free
cylinders with allowance for self-gravitation. Fluid Dyn. 26, No.5, 729-737, 1991
(transl. from Russian, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 5, 1991).
12. Shtemler Y., Stability of unsteady viscous flows, Fluid Dynamics, 4,601-604, 1981
(transl. from Russian, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 4, 1981).
13. Shtemler Y., Stable nonlinear waves in Poiseuille flow. Fluid Dynamics, 5, 669-673, 1978
(transl. from Russian, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 5, 1978).
14. Herzenstein S., Shtemler Y., Nonlinear growth of perturbation in boundary layers
and their stability. Soviet Physics Doklady, 234, 6, 300-302, 1977
(transl. from Russian, Doklady Akad. Nauk SSSR, 6, 1977).
15. Shreiber I.R., Shtemler Y., Origin, absorption and dispersion of noises in towed
underwater acoustic systems, Report of Inst. Ind. Math., Beersheva, Israel, 1999.
16. Pridor A., Shreiber I.R., Shtemler Y., Wet stack study,
Report of Inst. Ind. Math., Beersheva, Israel, 1996.
17. Gredeskul S., Shtemler Y., Vainberg Y., Clearing of a passage through a minefield.
Report of Inst. Ind. Math., Beersheva, Israel, 1993.
18. Chernyavski V., Shtemler Y., The modification of Galerkin method, Moscow Univ.,
Inst. of Mechanics, Reports 2750 & 2581, Moscow 1981 & 1982 (in Russian).