THE DESIGN OF WALLS, BINS, AND GRAIN ELEVATORS
CONTENTS INTRODUCTION COMMON PROBLEMS WITH BULK SOLIDS MILESTONES OF BULK SOLIDS TECHNOLOGY REFERENCES FUNDAMENTALS PARTICLES OR CONTINUUM? FORCES AND STRESSES THE BEHAVIOR OF POWDERS AND BULK SOLIDS (INTRODUCTION) THE MOHR STRESS CIRCLE INTRODUCTION OF THE MOHR STRESS CIRCLE DERIVATION OF THE MOHR STRESS CIRCLE BULK DENSITY, POROSITY AND DEGREE OF SATURATION BUOYANCY ELASTIC AND PLASTIC DEFORMATION ADHESIVE FORCES IN?UENCE OF PARTICLE SIZE ON THE BEHAVIOR OF A BULK SOLID PARTICLE SIZE DISTRIBUTION (PSD) CUMULATIVE DISTRIBUTION AND DENSITY DISTRIBUTION TYPE OF QUANTITY CHARACTERISTIC VALUES OF PARTICLE SIZE DISTRIBUTIONS CONVERSION OF THE TYPE OF QUANTITY PERMEABILITY APPLICATIONS IN BULK SOLIDS HANDLING VISCOUS FLOW (LAMINAR FLOW) IN?UENCE OF POROSITY TRANSITION TO INERTIAL FLOW (TURBULENT FLOW) FLOW PROPERTIES OF BULK SOLIDS UNIAXIAL COMPRESSION TEST CONSOLIDATION OF BULK SOLIDS TIME CONSOLIDATION FLOWABILITY REPRESENTATION OF STRESSES USING MOHR STRESS CIRCLES PRINCIPLES OF SHEAR TESTING TEST PROCEDURE YIELD LOCUS AND FLOW PROPERTIES TIME CONSOLIDATION (CAKING) WALL FRICTION TEST PROCEDURE FOR WALL YIELD LOCI WALL YIELD LOCUS AND WALL FRICTION ANGLE TIME WALL YIELD LOCUS, STATIC WALL FRICTION NUMBERS TO CHARACTERIZE FLOWABILITY FLOWABILITY FF C REMARKS ON THE TERM “FLOWABILITY” FURTHER NUMBERS TO INDICATE FLOWABILITY PRACTICAL DETERMINATION OF FLOW PROPERTIES MEASUREMENT WITH SHEAR TESTERS MEASUREMENT OF YIELD LOCI WITH THE JENIKE SHEAR TESTER MEASUREMENT OF YIELD LOCI WITH THE RING SHEAR TESTER MEASUREMENT OF TIME CONSOLIDATION MEASUREMENT OF KINEMATIC WALL FRICTION MEASUREMENT OF STATIC WALL FRICTION ATTRITION TEST COMPRESSIBILITY TEST SELECTION OF STRESSES YIELD LOCUS (FLOWABILITY) TIME YIELD LOCUS (FLOWABILITY AFTER TIME CONSOLIDATION) WALL YIELD LOCUS (WALL FRICTION) APPLICATION-RELATED MEASUREMENT OF FLOW PROPERTIES COMPARATIVE TESTS SILO DESIGN FOR FLOW A MORE DETAILED LOOK AT PROPERTIES OF BULK SOLIDS ANISOTROPY AND IN?UENCE OF DEFORMATION ON STRESSES STRESSES BULK DENSITY UNCON?NED YIELD STRENGTH (COMPRESSIVE STRENGTH) SHEAR DEFORMATION, SHEAR ZONES, LOCALIZATION IDEALIZATION: SIMPLE SHEAR AND PURE SHEAR SHEAR ZONES AND SHEAR BANDS DILATANCY STEADY-STATE FLOW AND DILATION DURING FLOW PROPERTY TESTING YIELD LOCUS PRESHEAR POINT, SHEAR POINTS AND MOHR STRESS CIRCLES TENSILE STRENGTH AND COHESION FLOW PROPERTIES AT VERY SMALL STRESSES IN?UENCE OF VELOCITY DISCUSSION OF TESTERS AND TEST PROCEDURES IN?UENCES ON TEST RESULTS PROCEDURE AND PRINCIPAL STRESSES STRESSES IN THE MEASURING PLANE REQUIREMENTS FOR TESTERS TO MEASURE FLOW PROPERTIES MEASURING TECHNIQUES AND EQUIPMENT (OVERVIEW) FUNNEL ANGLE OF REPOSE AVALANCHING IMSE TEST CARR FLOWABILITY INDEX STIRRER COHESION TESTER, FLOWABILITY TEST PENETRATION AND INDENTATION TESTS MONOAXIAL SHEAR TEST POWDER BED TESTER WITH TENSILE STRENGTH TEST UNIAXIAL TENSILE STRENGTH TEST TENSILE STRENGTH TEST WITH GAS FLOW JOHANSON HANG-UP INDICIZER™, SIMILAR TECHNIQUES QUALITY CONTROL TESTER BIAXIAL COMPRESSION TEST CONSTANT-VOLUME SHEAR TESTER JENIKE SHEAR TESTER TORSIONAL SHEAR TESTER RING SHEAR TESTER REMARKS ON RELIABILITY AND ACCURACY MEASUREMENT OF ADHESIVE FORCES SUMMARY PROPERTIES EXHIBITED BY SOME BULK SOLIDS EFFECTS IN FLOWING BULK SOLIDS STICK-SLIP BEHAVIOR VARIATION OF WALL FRICTION WITH DISPLACEMENT AND POSITION PARAMETERS AND CONDITIONS IN?UENCING FLOW BEHAVIOR PARTICLE SIZE DISTRIBUTION FLOW AGENTS LIQUIDS, MOISTURE GAS FLOW PARTICLE SHAPE FORMATION OF AGGLOMERATES EXAMPLES OF MEASURED FLOW PROPERTIES FLOW AGENT MOISTURE CONTENT TEMPERATURE PARTICLE SIZE ATTRITION STRESS DEPENDENCY OF WALL FRICTION IN?UENCE OF WALL MATERIAL ON WALL FRICTION ANGLE DIRECTION-DEPENDENT WALL FRICTION CALCULATION AND MEASUREMENT OF STRESSES IN BINS AND SILOS STRESS STATES IN SILOS RATIO OF HORIZONTAL TO VERTICAL STRESS STRESSES IN SILOS ASSESSMENT OF STRESSES STRESSES IN VERTICAL CHANNELS (JANSSEN’S APPROACH) FURTHER APPLICATION OF JANSSEN’S EQUATION BULK SOLID PROPERTIES FOR CALCULATION OF STRESSES WITH JANSSEN’S APPROACH CALCULATION OF STRESSES IN HOPPERS ESTIMATION OF STRESSES AT AN OUTLET OPENING BULK SOLID PROPERTIES FOR THE CALCULATION OF HOPPER STRESSES ASSESSMENT OF THE STRESS DISTRIBUTION IN A SILO LOADS ON FEEDERS VERTICAL STRESS AT AN OUTLET OPENING ESTIMATION OF DRIVING FORCES DISTURBANCES TO THE STRESS DISTRIBUTION LOCAL VARIATIONS OF THE CROSS-SECTION ECCENTRIC FLOW MEASUREMENT OF STRESSES IN BULK SOLIDS FLOW PRO?LES: MASS FLOW AND FUNNEL FLOW FLOW PROBLEMS IN SILOS JENIKE’S PROCEDURE FOR SILO DESIGN DESIGN OF MASS FLOW SILOS DESIGN OF FUNNEL FLOW SILOS OTHER APPROACHES TO ARCH FORMATION APPLICATION OF RESULTS DESIGN DIAGRAMS SILO CON?GURATIONS IN?UENCE OF FLOW PROPERTIES ON SILO CON?GURATION HOPPER CON?GURATIONS HOPPER SHAPE TRANSITIONS AND INCLINED WALLS MULTIPLE OUTLETS SPECIAL CASES: HOPPERS WITH VARYING STEEPNESS INSERTS INVERTED CONES AND WEDGES CONE-IN-CONE INSERT DISCHARGE TUBES DISCHARGE OF BULK SOLIDS MAXIMUM DISCHARGE RATE DISCHARGE RATE OF COARSE-GRAINED BULK SOLIDS DISCHARGE RATE OF FINE-GRAINED BULK SOLIDS DISCHARGE AIDS PNEUMATIC DISCHARGE AIDS MECHANICAL DISCHARGE AIDS APPLICATION OF DISCHARGE AIDS FEEDERS AND OTHER DISCHARGE DEVICES RULES FOR DESIGN REGARDING MASS FLOW TYPES OF DISCHARGE DEVICES (SELECTION) FEEDER DIMENSIONS AND PLACEMENT OF DISCHARGE AIDS SEGREGATION SEGREGATION MECHANISMS SIFTING AND OTHER SEGREGATION MECHANISMS ON INCLINED SURFACES PERCOLATION IN PARTICLE BEDS EFFECT OF AIR RESISTANCE TECHNIQUES TO REDUCE SEGREGATION MODI?CATION OF THE BULK SOLID OPTIMIZATION OF THE FILLING PROCESS REMIXING MIXING AND SEGREGATION ASSESSMENT OF MIXTURES SAMPLING SELECTED APPLICATIONS FINAL REMARKS SILO QUAKING AND SILO HONKING PHENOMENON CAUSES AND EFFECTS SHOCKS AS A RESULT OF SUDDEN FLOW SUDDEN FLOW AND PULSATING FLOW CAUSED BY STICK-SLIP FRICTION SHEAR ZONES IN SILOS ACCELERATION AND DECELERATION WAVES SILO SHOCKS DUE TO FLOW OF THE BULK SOLID SHEAR ZONES IN FLOWING BULK SOLID UNSTABLE STAGNANT ZONES (FUNNEL FLOW) FLOW AT THE SILO WALL COMBINATIONS OF DIFFERENT MECHANISMS SILO HONKING SHOCKS AND VIBRATIONS DUE TO OTHER REASONS LARGE DISCHARGE RATE WITH RESPECT TO OUTLET SIZE CYCLIC EXCITATION BY A FEEDER COLLAPSING ARCHES AND RATHOLES MEANS FOR REDUCING SILO QUAKING AND SILO HONKING REDUCTION OF THE ACCELERATED MASS REGULAR INITIATION OF SMALL SHOCKS INCREASING ROUGHNESS OF THE VERTICAL SECTION REDUCTION OF VELOCITY GRADIENTS TRANSFORMING FUNNEL FLOW INTO MASS FLOW SAMPLE PROBLEMS AND SOLUTIONS GENERAL REMARKS SAMPLE PROBLEMS SAMPLE PROBLEM 1: STRESSES IN THE VERTICAL SECTION OF A SILO SAMPLE PROBLEM 2: MAXIMUM STRESS IN A MASS FLOW SILO SAMPLE PROBLEM 3: DISCHARGE TUBE SAMPLE PROBLEM 4: DRIVING FORCE OF A FEEDER SAMPLE PROBLEM 5: PRESS SAMPLE PROBLEM 6: STRESSES IN COMBINED BINS SAMPLE PROBLEM 7: STRESSES IN FIBCS AND SACKS ON PALLETS SAMPLE PROBLEM 8: DISCHARGE RATE OF A COARSE BULK SOLID SAMPLE PROBLEM 9: SELECTION OF A WALL MATERIAL FOR MASS FLOW SAMPLE PROBLEM 10: DESIGN OF A MASS FLOW SILO SAMPLE PROBLEM 11: DESIGN OF A FUNNEL FLOW SILO SAMPLE PROBLEM 12: DESIGN OF A SILO UNDER CONSIDERATION OF TIME CONSOLIDATION REFERENCE SYMBOLS