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Nonlinear Wave Mechanics and Technologies

978-1-56700-305-5 (Print)
978-1-56700-346-8 (Online)

Nonlinear Wave Mechanics and Technologies

Rivner F. Ganiev
Institute of Machine Science named after A. A. Blagonravov, Russian Academy of Sciences Moscow, Russia

Leonid E. Ukrainskiy
Institute of Machine Science named after A. A. Blagonravov, Russian Academy of Sciences Moscow, Russia


This book is devoted to a systematic statement of the foundations of nonlinear wave mechanics - a new branch of mechanics, which is a scientific basis for wave technologies, having no analogues in world practice.
The results of application of wave technologies in most cases cannot be obtained in practice by the methods known at present, concerning the quality of the materials and products, the power inputs (a high quality of the products obtained using wave technologies is achieved at a significant reduction of power inputs), and other indicators.
Necessity to implement the wave of technologies in practice has led to the development of a new area of mechanical engineering - a wave engineering.
The main results (non-classical formulations of the problems, methods of investigation, new relationships of wave and oscillating processes in multiphase systems, wave mechanisms of motions and of stabilization, wave and oscillating phenomena and effects), presented in details in this book, show quite conclusively, that a number of wave phenomena and effects can hardly be obtained (even using the most ultimate modern supercomputers) without successful preliminary analytical procedure of establishment of the modes of motion. Here, analytics provides a clear understanding of physics and mechanics of nonlinear wave phenomena. These moments are likely to be taken as a rather natural approach by physicists and engineers delved into complex nonlinear wave and oscillating processes, especially at the conditions of nonlinear resonances. Certainly, in order to solve successfully such complex problems, it is necessary to reveal a certain art while formulating the problems on mechanics, based on the experience of work in the field of nonlinear oscillations and practical observations over oscillating and wave processes.

580 pages, © 2012

Table of Contents:

I. Formulation of the Problems in Nonlinear Wave Mechanics (Nonlinear Oscillations of Multiphase Systems) and Wave Technologies
II. Wave Mechanisms of Motions; Forces of Wave Nature; Modes of Motions; Nonlinear Resonances
A. Solid Particles Suspended in the Inhomogeneous Field of Fluid Flow
B. Bubbles Suspended in a Liquid Inside the Wave Fields
C. Nonlinear Resonance Relationships
D. Gas Inclusions in Capillaries and Pipes Filled by a Liquid
E. Viscous Fluid in Channels with Deforming Walls
F. Porous Medium Saturated with a Fluid
III. Wave Stabilization, Laminarization, and Turbulization of the Flows of Viscous Fluid; Wave Approaches to the Noiselessness of Structures with a Fluid and to the Drag Reduction
A. Flexible and Permeable Coatings of the Walls of Plane Flows; Wave Stabilization and Destabilization of Plane Flows in Channels and Boundary Layers
B. Flexible Coatings of Cylindrical Pipes; Instability against Small Disturbances; Nonlinear Stabilization
C. Stabilization and Suppression of Elastic Waves in Pipelines
IV. Scientific Basis for the Wave Machines and Apparatus; Nonlinear Generation of Oscillations and Waves, Wave Generators-Crucial Components (“Drivers”), Specifying the Operating Processes in Wave Machines
A. Viscous Fluid in Channels with High-Drag Elements; Modes of Mixing and Cavitational Dispersion
B. Swirling Cavitating Flows; Scientific Basis of Powerful Vortex Generators of Waves
C. Wave Machines with a Moving Operating Part and External Drive; Resonant Modes
D. Wave Machines for the Treatment of High-Viscous Media; Wave Effects while Creating Shear Deformations
V. Basis of Wave Mechanochemistry; Wave Mechanochemical Effects; Material Science; Wave Nanotechnology of Materials
A. Anomalous Decrease in the Viscosity of Cement Raw Materials under Wave Influence
B. Increase in Mobility of Cement Mortars under Wave Influences and Increase in Cement Stone Strength
C. Production of Stable Acrylic Dispersions under Wave Influences
D. Other Spheres of Possible Application of Wave Technologies in the Field of Physical and Chemical Transformations
VI. Wave Technologies of Oil-and-Gas Production and of the Increase in Oil-and-Gas Condensate Recovery of Reservoirs
A. Application of Wave Technology in Drilling
B. Wave Fields in Bottom-Hole Zones of the Bed; Oil Well Generators of Waves; Refinement of Bottom-Hole Zones and Horizontal Wells
C. Resonant Pumping of Wave Energy in a Bed; a Real Wave Treatment; Shock Wave Generator
D. Elimination of the Bridges of Retrograde Condensate in a Gas-Condensate Reservoir
E. Perspective Wave Technologies for the Increase of a Hydrocarbonic Recovery of Beds; Wave Mechanochemical Methods
VII. Wave Technologies for the Processes of Mixing, Separation, and Classification; Solution of the Problems of Engineering, Material Science, Ecology, Energy Sector, and other Industries; Wave Machines and Apparatus
A. Wave Homogenization, Mixing, and Separation of Liquid Mixtures, Emulsions, and Suspensions by Densities and Disperse Elements
B. Wave Technologies for the Performance of Processes in Porous Media, Saturated with a Liquid; Membrane Technologies; Impregnation; Refinement of Filters
C. Wave Technologies of the Processes of Dispersion of a Gas into Liquids; Applications in Ecology and Chemical Technologies
1. Motion of Solid Particles Suspended in Fluid in Wave Fields—Multiphase Mathematical Model of the System and Wave Effects
1.1. On the Dynamics of Solid Particles Suspended in an Incompressible Fluid Under Vibration Action; Wave Forces; Dynamic Modes and Their Stability
1.1.1. Problem Statement: Multiphase Medium “Fluid—Solid Particles,” Wave Forces
1.1.2. Particle Motion Inside a Cavity Under Vibration Actions; Added-Mass Mode; Intensification of the Processes of Separation and Mixing
1.1.3. Particle Motion Inside the Cavity Under Vibration Actions; Viscous Mode; Separation of the Particles According to Their Sizes
1.1.4. The Case When the Frequencies of the Oscillations along All the Axes are Equal; Added-Mass Mode; Mixing and Separation
1.1.5. Equality of the Oscillation Frequencies along All Three Axes; Viscous Mode, Mixing and Separation
1.1.6. The Case When the Cavity Rotates around One of the Axes and Executes Angular Oscillations around the Other Two Axes; Added-Mass Mode
1.2. On the Motion of Solid Particles, Suspended in the Wave Fields in the Compressible Medium; Wave and Oscillation Phenomena
1.2.1. Motion Equations and Problem Statement
1.2.2. Added-Mass Mode
1.2.3. Viscous Mode
1.2.4. Motion of Solid Particles in a Standing Plane Wave
1.2.5. Motion of Solid Particles in a Traveling Plane Wave
1.2.6. Motion of Solid Particles in the Traveling Spherical Wave
1.3. Conclusions
2. Dynamics of Bubbles in Fluid in Wave Fields: Mathematical Statement of the Problem about Dynamics of the Multiphase Medium “Liquid-Gas”—Wave and Oscillatory Effects
2.1. Motion of Bubbles in Vibrating Vessels and Wave Fields
2.1.1. Experimental Investigations of Bubble Motion in Wave Fields: Phenomenon of Wave Turbulization
2.1.2. Investigation of Spectral Characteristics of Pressure Pulsations at Oscillatory Phenomena in the System Liquid-Gas
2.2. On 3D Bubble Motion Modes and Conditions of Their Penetration in a Vibrating Liquid with a Free Surface
2.2.1. Problem Statement: Mathematical Model
2.2.2. Modes of One-Direction Motions of Bubbles Due to the Waves on the Liquid Free Surface
2.2.3. Mixing of Liquid Media with Bubbles in the Vibrating Cavities with a Free Surface, Gassing, Elimination of the Areas Unavailable for Bubbles. Estimation Technique of the Parameter Influence on These Processes
2.3. Dynamic Behavior of Gas Inclusions in a Vibrating Viscous Liquid
2.3.1. Statement of the Problem to Reveal the One-Direction Bubble Motions
2.3.2. Bubble Drift in a Vibrating Viscous Liquid
2.3.3. Analysis of Possible Modes of One-Direction Motions of Bubbles
2.4. Motion of Gas Inclusion in a Capillary under the Action of Vibration: Applications to the Problem of Motion of Gas Inclusions in Porous Media Saturated by a Liquid, and in Fuel Supply Systems
2.4.1. Mathematical Statement of the Problem
2.4.2. Model Analysis of Motion Modes of Gas Inclusions in a Capillary from the Rest Positions in Case of Main Resonance
2.4.3. Equations for Small Deviations from the Initial Position
2.4.4. Possible Modes of the Gas Inclusion Motion from the Initial Positions with Zero Velocities at the Initial Stage in a Horizontal Capillary
2.4.5. Model Analysis of the Wave Displacement of Gas from the Pores and Fractures of the Porous Media
2.4.6. Model Analysis of the Wave Displacement of Liquid from Porous Media
2.4.7. Model Analysis of the Wave Motion of Gas Inclusions in Vibrating Pipelines
2.4.8. Numerical and Experimental Investigations of the Motion of Gas Inclusions in Oscillating Capillaries
2.4.9. Results of Calculation of Gas Inclusion Dynamics in Typical Systems of Fuel Supply in Liquid-Propellant Engines
2.4.10. On the Self-Oscillations in an Elastic-Liquid System Accompanied by the Rise of Liquid: Application to the Question About Wave Intensification of Gas Lift
2.5. Conclusions
3. Wave Stabilization, Laminarization, and Turbulization of the Flows of Viscous Fluid: Wave Approaches to the Improvement of Reliability and Ensuring Noiseless Designs with a Fluid, and to the Reduction of Wall Friction. Acceleration of Fluid Motion in Capillaries and Porous Media asWell as in Granulated Solids by Means of the Waves
3.1. Flexible Wall Coatings of Plane Flows: Wave Stabilization and Destabilization of Plane Flows in Channels and Boundary Layers and Laminarization
3.1.1. Computational Criteria for the Appraisal of Laminarizing Coating Efficiency
3.1.2. Formulation of the Problem of Small Disturbances of the Poiseuille Flow in a Plane Channel with ElasticWalls: Direct and ObliqueWaves of Disturbances
3.1.3. Stabilization and Destabilization of Disturbances in the Poiseuille Flow between Compliant Plates
3.1.4. Formulation of the Problem of Small Disturbances on a Compliant Wall
3.1.5. Main Results for Model Investigations of Boundary Layer Stability Compliant Plates with Laminarizing Coatings in Flow
3.2. Stability of Plane Flows with Permeable Boundaries
3.2.1. Formulation of the Problem on Small Disturbances of the Poiseuille Flow in a Plane Channel with Permeable Walls and in the Boundary Layer on a Flat Smooth Permeable Plate
3.2.2. Boundary Layer without Accounting for the Flow in the Gap
3.2.3. Boundary Layer Accounting for the Flow in the Gap
3.2.4. Poiseuille Flow with Permeable Boundaries
3.2.5. Experimental Verification of the Theoretical Results
3.2.6. Conclusions about the Capability of Permeable Walls to Laminarize or Turbulize the Flow
3.3. Hydrodynamic Stability of the Poiseuille Flow in Circular Compliant Pipes
3.3.1. Formulation of the Problem Concerning Infinitely Small Wave Disturbances
3.3.2. Linear Destabilization
3.4. Nonlinear Problem of the Propagation of Finite Disturbances of the Poiseuille Flow in a Circular Compliant Pipe: Monoharmonic Self-Oscillaltions and Secondary Flows
3.4.1. Formulation of the Problem
3.4.2. Calculation Technique
3.4.3. Wave Forms of Self-Oscillations
3.4.4. Secondary Flows
3.4.5. Direction of Bifurcation: Hard and Soft Excitations of Self-Oscillationss
3.4.6. Conclusions
3.5. Experimental Investigation of the Flow of Fluid in Pipelines with Compliant Walls
3.5.1. Technique of Experimental Investigations
3.5.2. Structure of Pipeline Internal Coatings
3.5.3. Results of the Experiments: Dependence of the Pipeline Hydraulic Drag on the Wall Compliance
3.6. Transformation of the Wave Motions of Fluid and Granulated Solids into One-Directional Motions
3.6.1. On Fluid Dynamics in Thin Pipes and Capillaries with Deformable Walls under Wave Excitations
3.6.2. Resonance Effects of Intensification of a Granular Material Displacement by a Modulated Flow of Carrying Gas: Application in Fire-Fighting Units
3.7. Scientific Basis forWave Technologies of Reliability Enhancement and Acoustic Noise Reduction of Pipelines: Stabilization of Elastic Waves in Pipelines
3.7.1. Protection of Pipeline Systems from the Action of Hydraulic Shocks
3.7.2. Stabilization of Acoustic Waves in the Pipelines: Vibroprotection and Noise Cancellation
3.7.3. Application of Stabilizers of Wave Processes in Oil-Producing Industry Pipeline Systems
3.7.4. Conclusions
4. Wave Processes in Porous Mediums Saturated with Liquid.Wave Methods to Accelerate Filtration. Generation of Additional Filtration Flows
4.1. Propagation of NonlinearWaves in Porous Medium Saturated with Liquid. Possibilities to Reduce Damping. Resonance Transfer of Wave Energy
4.1.1. Derivation of the Burgers Equation
4.1.2. Dependence of the Burgers Equation Coefficients on the First Lame Parameter
4.1.3. Influence of Nonlinearity on the Wave Propagation. Nonlinear Parametric Interaction
4.2. On the Resonance Character of the Wave-Field Amplitude Distribution in the Bottomhole Formation Zone
4.2.1. Problem Statement
4.2.2. Solution Technique
4.2.3. Calculation Results. Resonance Amplification of Vibrations in the Porous Mediums with Perforation Channels
4.2.4. Resonance Distribution of Amplitudes in the Annular Axisymmetric Areas Simulating the Wellbottom Zone
4.3. Forced Nonlinear Oscillations of the Porous Medium Saturated with Liquid. Resonance
4.3.1. Statement of the Problem Regarding Forced Oscillations of a Part of the Medium
4.3.2. Abnormally Large Filtration Flows Caused by the Waves
4.3.3. Summary
4.4. Experimental Investigations of Filtration Control by Means of the Wave Effects
4.4.1. Cleaning of the Porous Medium from Inclusions in the Form of Solid Particles in the Pores. Scientific Basis for the Wave Technology of Cleaning the Wellbottom Zones
4.4.2. Generation of Poorly Permeable Local Areas in Porous Mediums Saturated with Liquid. Scientific Basis of Well Colmatation While Drilling
4.5. Conclusions
5. Scientific Basis of Wave Machines and Devices; Nonlinear Generation of Vibrations and Waves; Mixing in Viscous Liquid Flows; Generators of Vibrations and Waves—Key Elements (“Drivers”) of Wave Machines
5.1. Viscous Liquid in Flat Channels with High-Drag Elements; Modes of Mixing and Cavitation Dispergation
5.1.1. Statement of the Problem about 2D Cavitation Flows of Liquid
5.1.2. Cavitation Fluxes in 2D Flows; Results of Simulation
5.1.3. Mixing in 2D Flows with High-Drag Elements; Mathematical Statement of the Problem
5.1.4. Estimation of Mixing in Enclosed Volumes
5.1.5. Estimation of Mixing in the Flows through the Channels with High-Drag Elements
5.1.6. Experimental Investigations of 2D Flows with High-Drag Elements; Scientific Basics of Flat Wave Generators
5.2. Swirl Cavitating Flows; Scientific Basics of Powerful Vortex Generators of Waves
5.2.1. Mathematical Statement of the Problem
5.2.2. Emergence of Toroidal Vortices
5.2.3. Emergence of Cavitation Areas and the Cavitation Method of the Vibration Excitation
5.2.4. Vibrations Caused by the Toroidal Vortex Drifting and Separation at the Laminar Flows; Reverse Flows
5.2.5. Mixing in Swirl Flows
5.2.6. Hydraulic Drag of Generators
5.2.7. Experimental Investigations of Generators
5.2.8. Conclusions
5.3. Wave Dispergation of Liquid in Swirl Flows
5.3.1. Experimental Facility
5.3.2. Amplitude-Frequency Characteristics
5.3.3. Technique of Measuring the Sizes of Air Bubbles in Water
5.3.4. Average Sizes of Gas Bubbles
5.3.5. Conclusions
5.4. Low-Frequency Impactor Generators
5.4.1. Calculation of the Interface Velocity
5.4.2. Estimation of the Boundary Motion Velocity and of the Impact Force of the Falling Fluid Column on a Fixed Barrier with Account of the Friction Force
5.4.3. Drop of the Liquid Column of Finite Length in the Presence of Gravity
5.4.4. Calculation Results
5.4.5. Conclusions
5.5. Wave Machines with a Moving Body; Resonance Regimes
5.5.1. Resonance Electromechanical Vibration Generators
6. Principles of Wave Mechanochemistry. Wave Mechanochemical Effects. Material Science and Chemical Technologies. Wave Technologies of Building Materials Production. Wave Nanotechnologies
6.1. Anomalous Reduction in the Cement Material Viscosity under Wave Effects
6.1.1. Test Facility for the Investigation of Cement Raw Material Flow in the Pipelines
6.1.2. Results of the Experiments
6.2. Increase in the Flowability of Cement Mortars under the Wave Impact and Increase in the Cement Stone Strength
6.2.1. Technique of the Experiments
6.2.2. Water-cement Mixtures and Building Mortars: Enhancements in Strength, Flowability, and Water Resistance
6.2.3. Wave Impact on the High-Sand Mixtures, Influence of Plasticizers, and Nonlinear Enhancement of Flowability
6.3. Wave Technologies of Mixing; Homogenization of Mortars, Emulsions, and Suspensions for the Energy Sector of Industry
6.3.1. Production of Mixed Fuels
6.3.2. Advantages of the Application of Water–Fuel Oil Emulsions at Fuel Storage and Combustion
6.3.3. Experimental Investigation of the Emulsification Processes Occurring Owing to the Effects of Nonlinear Wave Mechanics
6.3.4. Results of Laboratory Experiments
6.3.5. Industrial Tests of the Combustion of Fuel Oil and Preliminary Prepared Water–Fuel Oil Emulsions
6.3.6. Industrial Tests of Combustion of the Water-Fuel Emulsion Obtained Immediately before the Combustion
6.3.7. Water-Gas-Condensate Emulsion Firing at Oil and Gas Drilling Sites
6.4. Introduction to theWave Technology of Nanomaterials and Obtaining of Nanosilica
7. Wave Technologies for Oil and Gas Production and Enhancement of Oil–Gas–Condensate Recovery of Reservoirs: Development of Wave Equipment
7.1. Application of Wave Technology in Drilling
7.1.1. Wave Effects, Applied to the Development of Devices for Well Colmatation, Increase in the Mechanical Rate of Drilling, and Treatment of WBZs from Drilling Mud Filtrate
7.1.2. Theoretic Investigation of Wave Generator Hydrodynamics as Applied to Drilling Problems
7.1.3. Field Tests of Drilling Wave Technology
7.1.4. Improvement of Drill Mud Quality: Control of Cement Slurry Properties
7.1.5. Conclusions about the Prospects of Application of Wave Technology in Drilling
7.2. Wave Fields in the Bottom-Hole Formation Zones:WellboreWave Generators, Cleaning of Bottom-Hole Formation Zones, and Horizontal Wells for Increase in Oil Production
7.2.1. Treatment Scheme of WBZs in Injection and Production Wells
7.2.2. Pilot-Field Tests on Cleaning Bottom-Hole Formation Zones Near Production Wells
7.2.3. Pilot-Field Tests on Cleaning Bottom-Hole Formation Zones Near Injection Wells
7.2.4. Experiments on the Treatment of Bottom-Hole Formation Zones of Horizontal Wells
7.3. Wave Technology for Intensification of Gas-Lift Extraction of Oil
7.4. Resonant Injection of Wave Energy in the Reservoir: Real Wave Treatments and Increase in Reservoir Recovery
7.4.1. Treatments of Pools by Periodical Shock Waves
7.4.2. Responsive Blocks of Wells
7.5. Liquidation of Plugs of Retrograde Condensate in Gas–Condensate Beds
7.5.1. Mathematical Model Describing the Origination of Retrograde Gas–Condensate Plugs and the Influence of the Waves
7.5.2. Process of Liquid Plug Formation
7.5.3. Pressure Oscillations Impact on Gas–Condensate Beds: Increase in Production Well Debit
7.5.4. Self-Oscillations in Natural Gas–Condensate Beds
7.5.5. Wave Impact of the Self-Oscillating Mode of the Flow
7.5.6. Wave Impact without of Self-Oscillations
7.5.7. Experimental Modeling of Non-Stationary Processes in Gas–Condensate Beds
7.5.8. Conclusions
7.6. Promising Wave Technologies for the Increase of Hydrocarbon Productive Capacity in Reservoirs: Wave Mechanochemical Methods and Wave Effects on Water-Flooded Pools
8. Wave Machines and Devices: TypicalWave Technologies
8.1. Drivers of Wave Machines and Devices: Hydrodynamic Wave and Vibration Generators and Resonance Electromechanical Oscillation Generators
8.2. Laboratory and Research Facilities:Wave Rigs and Equipment and High-Efficiency ResonanceWave Devices (Units) of Mixing, Homogenization, Dispersion, and Activation
8.2.1. Spacial Mixing
8.2.2. Production of Water–Oil Emulsions
8.2.3. Spatial Mixing and Homogenization: Production of theWater–Oil Emulsion and Water–Gas–Oil System
8.2.4. Mixing of Powdered Materials
8.3. Wave Technologies and Wave Machines
8.3.1. Hydrodynamic Flowing Rigs and Wave Devices
8.3.2. Universal Flowing Mixer–Activator of Liquid Compositions
8.3.3. Combined Wave Mixer of Liquid Materials
8.3.4. Mixer–Activator of Dry Mixtures
8.3.5. Wave Separators of Multiphase Media
8.3.6. Jet Mill With a Flat Working Chamber
8.3.7. Classifiers
8.3.8. Multipurpose Centrifugal Pulsed-Wave Blender
8.4. Wave Technologies in Some Sectors of Modern Industry
8.4.1. Wave Technology in the Building Industry
8.4.2. Wave Technologies in the Area of Producing Nanomaterials
8.4.3. Intensification of Technological Processes in Chemistry, Oil Chemistry, and Oil Refining
8.4.4. Wave Technology in the Food Industry
8.4.5. Wave Technologies in Ecology
8.4.6. Wave Technology in the Oil Producing Industry
8.4.7. Wave Technologies in Mechanical Engineering
8.5. On Wave Technologies in Innovation Mechanical Engineering
8.5.1. Introduction: On the Possibilities and Prospects of Wave Technologies in Industry
8.5.2. Fine and Super-Fine Grinding and Activation of Materials
8.5.3. Mixing and Activation of Multicomponent Materials (Dry Mixtures)
8.5.4. Batching of Granular Components
8.5.5. Technologies for Production and Wave Processing of Emulsions, Suspensions, and Foams