ISBN 1er exemplaire : 978-3-527-31421-5
1 Introduction
2 Dimensional Analysis
2.1 The Fundamental Principle
2.2 What is a Dimension?
2.3 What is a Physical Quantity?
2.4 Base and Derived Quantities, Dimensional Constants
2.5 Dimensional Systems
2.6 Dimensional Homogeneity of a Physical Content
Example 1: What determines the period of oscillation of a pendulum?
Example 2: What determines the duration of fall thêta of a bod[...]
ISBN 1er exemplaire : 978-3-527-31421-5
1 Introduction
2 Dimensional Analysis
2.1 The Fundamental Principle
2.2 What is a Dimension?
2.3 What is a Physical Quantity?
2.4 Base and Derived Quantities, Dimensional Constants
2.5 Dimensional Systems
2.6 Dimensional Homogeneity of a Physical Content
Example 1: What determines the period of oscillation of a pendulum?
Example 2: What determines the duration of fall thêta of a body in a homogeneous gravitational field (Law of Free Fall)?. What determines the speed v of a liquid discharge out of a vessel with an opening? (Torricelli's formula)
Example 3: Correlation between meat size and roasting time
2.7 The Pi Theorem
3 Generation of Pi-sets by Matrix Transformation
Example 4: The pressure drop of a homogeneous fluid in a straight, smooth pipe (ignoring the inlet effects)
4 Scale Invariance of he Pi-space-the Foundation of the Scale-up
Example 5: Heat transfer from a heated wire to an air stream
5 Important Tips Concerning the Compilation of the Problem Relevance List
5.1 Treatment of Universal Physical Constants
5.2 Introduction of Intermediate Quantities
Example 6: Homogenization of liquid mixtures with different densities and viscosities
Example 7: Dissolved air flotation process
6 Important Aspects Concerning the Scale-up
6.1 Scale-up Procedure for Unavailability of Model Material Systems
Example 8: Scale-up of mechanical foam breakers
6.2 Scale-up Under Conditions of Partial Similarity
Example 9: Drag resistance of a ship's hull
Example 10: Rules of thumb for scaling up chemical reactors: Volume-related mixing power and the superficial velocity as design criteria for mixing vessels and bubble columns
7 Preliminary Summary of the Scale-up Essentials
7.1 The Advantages of Using Dimensional Analysis
7.2 Scope of Applicability of Dimensional Analysis
7.3 Experimental Techniques for Scale-up
7.4 Carrying out Experiments Under Changes of Scale
8 Treatment of Physical Properties by Dimensional Analysis
8.1 Why is this Consideration Important?
8.2 Dimensionless Representation of a Material Function
Example 11: Standard representation of the temperature dependence of the viscosity
Example 12: Standard representation of the temperature dependence of density
Example 13: Standard representation of the particle strength for different materiaIs in dependence on the particle diameter
Example 14: Drying a wet polymeric mass. Reference-invariant representation of the material function D(T, F)
8.3 Reference-invariant Representation of a Material Function
8.4 Pi-space for Variable Physical Properties
Example 15: Consideration of the dependence mu(T) using the muw/mu term
Example 16: Consideration of the dependence rhô(T) by the Grashof number Gr
8.5 Rheological Standardization Functions and Process Equations in Non-Newtonian Fluids
8.5.1 Rheological Standardization Functions
8.5.1.1 Flow Behavior of Non-Newtonian Pseudoplastic Fluids
8.5.1.2 Flow Behavior of Non-Newtonian Viscoelastic Fluids
8.5.1.3 Dimensional-analytical Discussion of Viscoelastic fluids
8.5.1.4 Elaboration of Rheological Standardization Functions
Example 17: Dimensional-analytical treatment of Weissenberg's phenomenon Instructions for a PhD thesis
8.5.2 Process Equations for Non-Newtonian Fluids
8.5.2.1 Concept of the Effective Viscosity mueff According to Metzner-Otto
8.5.2.2 Process Equations for Mechanical Processes with Non-Newtonian Fluids
Example 18: Power characteristics of a stirrer
Example 19: Homogenization characteristics of a stirrer
8.5.2.3 Process Equations for Thermal Processes in Association with Non-Newtonian Fluids
8.4.2.4 Scale-up in Processes with Non-Newtonian Fluids
9 Reduction of the Pi-space
9.1 The Rayleigh - Riabouchinsky Controversy
Example 20: Dimensional-analytical treatment of Boussinesq's problem
Example 21: Heat transfer characteristic of a stirring vessel
10 Typical Problems and Mistakes in the Use of Dimensional Analysis
10.1 Model Scale and Flow Conditions - Scale-up and Miniplants
10.1.1 The Size of the Laboratory Device and Fluid Dynamics
10.1.2 The Size of the Laboratory Device and the Pi-space
10.1.3 Micro and Macro Mixing
10.1.4 Micro Mixing and the Selectivity of Complex Chemical Reactions
10.1.5 Mini and Micro Plants from the Viewpoint of Scale-up
10.2 Unsatisfactory Sensitivity of the Target Quantity
10.2.1 Mixing Time thêta
10.2.2 Complete Suspension of Solids According to the 1-s Criterion
10.3 Model Scale and the Accuracy of Measurement
10.3.1 Determination of the Stirrer Power
10.3.2 Mass Transfer in Surface Aeration
10.4 Complete Recording of the Pi-set by Experiment
10.5 Correct Procedure in the Application of Dimensional Analysis
10.5.1 Preparation of Model Experiments
10.5.2 Execution of Model Experiments
10.5.3 Evaluation of Test Experiments
11 Optimization of Process Conditions by Combining Process Characteristics
Example 22: Determination of stirring conditions in order to carry out a homogenization process with minimum mixing work
Example 23: Process characteristics of a self-aspirating hollow stirrer and the determination of its optimum process conditions
Example 24: Optimization of stirrers for the maximum removal of reaction heat
12 Selected Examples of the Dimensional-analytical Treatment of Processes in the Field of Mechanical Unit Operations
Introductory Remark
Example 25: Power consumption in a gassed liquid. Design data for stirrers and model experiments for scaling up
Example 26: Scale-up of mixers for mixing of solids
Example 27: Conveying characteristics of single-screw machines
Example 28: Dimensional-analytical treatment of liquid atomization
Example 29: The hanging film phenomenon
Example 30: The production of liquid/liquid emulsions
Example 31: Fine grinding of solids in stirred media mills
Example 32: Scale-up of flotation cells for waste water purification
Example 33: Description of the temporal course of spin drying in centrifugaI filters
Example 34: Description of particle separation by means of inertial forces
Example 35: Gas hold-up in bubble columns
Example 36: Dimensional analysis of the tableting process
13 Selected Examples of the Dimensional-analytical Treatment of Processes in the Field of Thermal Unit Operations
13.1 Introductory Remarks
Example 37: Steady-state heat transfer in mixing vessels
Example 38: Steady-state heat transfer in pipes
Example 39 Steady-state heat transfer in bubble columns
13.2 Foundations of the Mass Transfer in a Gas/Liquid (G/L) System
A short introduction to Examples 40, 41 and 42
Example 40: Mass transfer in surface aeration
Example 41: Mass transfer in volume aeration in mixing vessels
Example 42: Mass transfer in the G/L system in bubble columns with injectors as gas distributors. Otimization of the process conditions with respect to the efficiency of the oxygen uptake E=G j/sigmaP
13.3 Coalescence in the Gas/Liquid System
Example 43: Scaling up of dryers
14 Selected Examples for the Dimensional-analytical Treatment of Processes in the Field of Chemical Unit Operations
Introductory Remark
Example 44: Continuous chemical reaction process in a tubular reactor
Example 45: Description of the mass and heat transfer in solid-catalyzed gas reactions by dimensional analysis
Example 46: Scale-up of reactors for catalytic processes in the petrochemical industry
Example 47: Dimensioning of a tubular reactor, equipped with a mixing nozzle, designed for carrying out competitive-consecutive reactions
Example 48: Mass transfer limitation of the reaction rate of fast chemical reactions in the heterogeneous material gas/liquid system
15 Selected Examples for the Dimensional-analytical Treatment of Processes whithin the Living World
Introductory Remark
Example 49: The consideration of rowing from the viewpoint of dimensional analysis
Example 50: Why most animaIs swim beneath the water surface
Example 51: Walking on the Moon
Example 52: Walking and jumping on water
Example 53: What makes sap ascend up a tree?
16 Brief Historic Survey on Dimensional Analysis and Scale-up
16.1 Historic Development of Dimensional Analysis
16.2 Historic Development of Scale-up
17 Exercises on Scale-up and Solutions
17.1 Exercises
17.2 Solutions
18 List of important, named pi-numbers
19 References
Index
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