WATER JET CONFERENCE - Waterjet Technology Association

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system. Examples of the component matrices for a pipe section and a pipe junction will be presented. The equations of motion for a section of pipe are solved by assuming that the instantaneous pressure, H, and discharge, Q, are mean quantities (H o, Q o ) plus deviations from the mean (h, q). The deviations are assumed to be sinusoidal with respect to time. The flow rate and pressure on the left side of the (i+l)th section are obtained in terms of these quantities on the right side of the ith section as follows. and L Li qi +1 = cos ai L hi+1 = − jCi sin Li ai R j qi − sin Ci Li ai R Li qi + cos ai 5 R hi (1) R hi (2) Ci = ai (3) gAi where ai is the water hammer wave velocity in the ith pipe, g is the acceleration due to gravity, AI is the area of the pipe, Li is the length of the pipe and ω is the driving R frequency. The equation matrix for a length of pipe is composed of the coefficients of qi R and hi in Equations (1) and (2) above. Similar equations are obtained for each component in the modulator piping system. For example, at a series pipe junction where only the pipe size changes, the flow rate and the pressure are normally assumed to be constant. Therefore, the equations relating upstream quantities to those downstream are given by: L qi +1 = qi h i+1 L = O qi L + O hi L L ( ) + hi L ( ) (4) The equation matrix for a series pipe junction is the identity matrix since the coefficient in the equations above are either zero or one. When equation matrices for each component in the modulator are obtained they are multiplied in the proper order to produce two equations relating pressure and flow rate at the upstream boundary of the system to these quantities at the downstream boundary. At the system boundaries normally two of these quantities are known and the two equations can be used to solve for the remaining two unknowns. When the method is applied to the branch piping system shown in Figure 1, the following equations result (5)
R = a1 ⋅ A1 A2 a2 I = 2H o Q o ⎡ ⎣ ⎢ tan L 1 a 1 gA1 tan a1 L1 a1 ⋅sin L 2 a 2 ⋅cos L 2 a 2 R q3 = ⋅ cos L 3 a 3 q ⋅ cos L 3 a 3 R 2 + I 2 + a3 ⋅ A3 A2 sin a2 L2 a2 + gA 2 a 2 6 sin L 2 a 2 (6) ⋅sin L 3 a 3 ⋅ cos L 3 a 3 (7) − cos L 2 a 2 + gA 3 a 3 cos L 2 a 2 ⋅cos L 3 a 3 ⋅ sin L 3 a 3 where q is the amplitude of the input oscillation of flow, H o is the mean pressure at the nozzle, Q 0 is the mean flow rate and a i , A i , L i and ω are the wave speed, pipe area, pipe length and modulation frequency respectively. This equation can be used to calculate the response flow rate at the nozzle q 3 R for a given input oscillation of flow q for any modulator frequency ω. THE DIMENSIONLESS PIPE LENGTH APPROACH by: The arguments, Θ i of the trigonometric functions in Equations (7) and (8) are given Θ i = L i a i = 2 FL i a i where F is the driving frequency in cycles per second. Since the quantities in Equation (6) are squared, the trigonometric functions repeat their values every π radians. Therefore a dimensionless pipe length, M i can be defined as: M i = Θ i = 2FL i a i where all of the response information from Equation (6) is obtained as the dimensionless pipe lengths vary from zero to one. Since there are three dimensionless pipe lengths, the parametric study will be three-dimensional. Equation (6) was written in terms of the dimensionless pipe lengths and the amplitude of the modulated flow at the nozzle q 3 R non-dimensionalized with the mean flow Q 0 was calculated for the full range of dimensionless lengths. Contours of modulation response are presented versus dimensionless pipe lengths in Figures 2 through 6. The input oscillation was 20% of the mean flow for all of the calculations. Figures 3 and 5 show relatively large areas of modulation in excess of 20%. Contours up to 51% were plotted. (8) (9) (10) ⎤ ⎦ ⎥
Page 1 and 2: Proceedings of the Second U.S. WATE
Page 3 and 4: Visualization of the Central Core o
Page 5 and 6: A Status Report on the Conceptual D
Page 7 and 8: SESSION 7 - CIVIL & INDUSTRIAL Chai
Page 9 and 10: Cutting Hard Rock With Abrasive-Ent
Page 11: frictional and piping component rel
Page 15 and 16: attenuation of the output. The tran
Page 17 and 18: Figure 1. Branch System Modulator F
Page 19 and 20: Figure 5. Modulation Response for B
Page 21 and 22: Figure 9. Modulation response for s
Page 23 and 24: can be used for any form of input.
Page 25 and 26: with a cylindrical shape to the jet
Page 27 and 28: m/s. The range of power found from
Page 29 and 30: Figure 3. Power vs nozzle diameter
Page 31 and 32: Figure 5. Frequency vs length of th
Page 34 and 35: NAME: Gerald Zink COMPANY: StoneAge
Page 36 and 37: modulatornozzle assembly. The ordin
Page 38 and 39: DISCUSSION OF FLUID MECHANICS The i
Page 40 and 41: This process serves to protect the
Page 42 and 43: For test purposes, these concrete b
Page 44 and 45: REFERENCES CITED 1. Barker, C. R.,
Page 46 and 47: FIGURE 4. INNER CORE OF PERCUSSIVE
Page 48 and 49: FIGURE 9. EXAMPLE OF HIGH-PRESSURE
Page 50 and 51: NAME: John E. Wolgamott COMPANY: St
Page 52 and 53: THE FOCUSED SHOCK TECHNlQUE FORPROD
Page 54 and 55: The reflected wave is thus also cyl
Page 56 and 57: neglected. The introduction of a co
Page 58 and 59: DISCUSSION NAME: George Savanick CO
Page 60 and 61: H’ mean shape factor Hj theoretic
Page 62 and 63:
Required streamline curvature at th
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2 x 2 ≅ ( e − 2 p + w)/k2 (2-8)
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eliminating 2 n r 2 from equations
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approximation to the actual flow si
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skin friction coefficient but are c
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where: (H) = A1H 3 + A2H 2 + A3H +
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effect (< 0.5%) on coefficients of
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TABLE 5 Rei x 10 5 β 3 4 5 6 Po Po
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TABLE 6 D(mm) d o(mm) L t(mm) L f(m
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expanding rather than contracting a
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25. Weber, H.E., 1978, Boundary lay
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Figure 5. Wall velocity distributio
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Figure 9. Effect of nozzle design o
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Figure 12. CA+T Design Philosophy.
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Figure 16. Effect of inlet b 1 cond
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Figure 20. Relaminarization at nozz
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Figure 24. Pressure decay data. 88
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VISUALIZATION OF THE CENTRAL CORE O
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DISCUSSION Although employing the i
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5. Lambert, J. H., 1760, Photometri
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Figure 6. Spectral sensitivity curv
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NAME: W.C. Cooley COMPANY: Terraspa
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INTRODUCTION Pulsed liquid jets sho
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y=X ∨ P A dy = p p A p 2 (L c y=0
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Using equation (15), the value of X
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Thus about the first 10% of the dri
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Many design cases, including those
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surface spall occurred, resulting i
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Figure 3. Chamber pressure at pisto
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Figure 7. Effect of nozzle area rat
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Figure 11. Extrusion device schemat
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Figure 15. Typical chamber pressure
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DISCUSSION NAME: W. C. Cooley COMPA
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material which are, in turn, affect
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the water jet. This method was not
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where h is the depth of penetration
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obtained during this phase of the i
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observed that the smallest depth of
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Figure 2. Idealized Relationships b
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Figure 6. Penetration as a Function
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DEVELOPMENT OF VARIABLE DELIVERY TR
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THE STRUCTURE AND FUNCTION OF THE P
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The injection pressure can be contr
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ACKNOWLEDGEMENTS The authors gratef
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Figure 4. Theoretical required powe
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Figure 9. Variation of efficiency w
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THE "SKIPJACK" SEWER CLEANING NOZZL
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HYDRO-BLASTING SAFETY C.W. Adaway,
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Remember, your Hydro-Blasting work
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horizontal, sometimes vertical, and
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Figure 2. Safety Gear Figure 3. Tub
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DEVELOPMENTS IN CLEANING COKE OVEN
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causing chain breakages and the scr
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was encountered, then the rotation
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(C) Capital Expenditure: Material i
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Figure 9. Swivel coupling Figure 10
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OPTIMIZING JET CUTTING POWER FOR TU
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PRESSURE DROP (psi) ELEMENT Cv @10
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power output. Undersized nozzles re
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Subscripts n - Nozzle p - Pump t -
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Figure 1. Cutting effect as a funct
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CONSIDERATIONS IN THE COMPARISON OF
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pressure can be lowered to perhaps
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Figure 2: Fan jet issuing from a no
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DISCUSSION NAME: John Griffiths COM
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where Q = Flow rate - gpm D = Jet O
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Again, not limited to Newtonian flu
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REFERENCES 1. Brown, R.W. and Loper
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Table 2. Jet Cleaning Speeds and ot
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ANSWER: The utilization of the stat
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complexity and short component life
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Figure 4, for ap values ranging fro
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Decontamination Methods for rapidly
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a. “PULSER” b.”ORGAN-PIPE”
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Figure 5 - Removal rate for various
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DISCUSSION NAME: David A. Summers C
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DRILLING BORE HOLES IN COAL MINES U
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pile could not be judged as represe
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DISCUSSION NAME: David Summers COMP
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HYDRAULIC MINING EXPERIMENTS IN AN
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The monitor was fed pressurized wat
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The IH rig was considered to be sup
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REFERENCES 1. Okhrimenki, V. A., A.
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Figure 2. Jet cutting sandstone at
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Figure 5. Schematic plan view of In
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Figure 7. Suction Box. 226
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USE OF HIGH PRESSURE WATER JETS FOR
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flame torch to cut this block, redu
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the order of 360 rpm. Under these c
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Figure 3. Slot cut by jet at 11 o s
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JET-MINER SURFACE AND IN-SEAM TRIAL
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The hydraulic drive of the haulage
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The surface trials had have the obj
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Figure 2. Experimental version. Fig
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Figure. 7 Jet-Miner prototype Figur
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SOME PATTERNS OF TECHNOLOGY TRANSFE
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Development of High Pressure_Techno
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configurations, the design of an op
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and public sectors. After a haitus
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Souder, W.E. and Evans, R.J., "The
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Figure 5. Technological achievement
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Table 3. Perceived disadvantages of
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already been, or is being applied w
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Using the requirements profile and
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ant hose combination, a guiding sys
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HYDRAULIC MINING TESTS Site selecti
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SAFETY All operations were carried
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TABLE V. Categories of Jet Mining D
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Figure 2. Generalized geologic prof
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SECONDARY FRAGMENTATION WITH WATER
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do possess a maximum point (Fig. 8)
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Figure 4. Rossin-Rammler plot. Figu
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Figure 8. Non-dimensional plot for
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HYDRAULIC COAL MINING SYSTEM Typica
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Figure 4. (From ref. 1) DISCUSSION
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INTRODUCTION Developing an unique t
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The coefficients "b " in Eq. (1) ca
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By the end of 1982, a total of more
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Figure 4. Cutting ability of swing-
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Figure 10. An operating performance
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for an abrasive, the abrasive parti
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the particles, while at slower spee
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to break away the remaining segment
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Table 1. Concrete saw technology. T
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NAME: Tom Brunsing COMPANY: Foster-
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FEASIBILITY STUDY OF CUTTING SOME M
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hydraulic power required to cut thr
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pressure was varied from 103 to 310
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2.1 Heading and gutting fresh cod f
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Figure 5. The cuts surface of a blo
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Figure 17. Cuts made across the cla
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JET NOTCHING USED IN THE CONSTRUCTI
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Bottom notch diameter was determine
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σ H = in-situ stress in the horizo
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Figure 3. Final block displacement.
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Figure 8. Comparison of Slurry Pump
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THE FURTHER DEVELOPMENT OF AN UNDER
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use taps or hydrants. To achieve th
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supply line. It was determined that
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The rotating head requires major mo
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Figure 4. System field test set-up
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Figure 10. Bentonite drilled clay s
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MECHANICAL TOOLS Cutting Tool Energ
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Ψ = cos −1 ⎧ ⎪ ⎪ ⎨ ⎪
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mode also contributes to chip flush
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NAME: Simon Johnson COMPANY: Newcas
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ROLLER TOOLS COMBINED WITH HIGH-PRE
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Various designs and applications ar
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Figure 1. Full-face tunneling machi
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Figure 11. roadway profile cutting
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Figure 19. High-pressure water jet
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DESIGN AND OPERATION OF TWO LARGE-S
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The hydraulic system for the thrust
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Results of Trial Tests As part of m
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cutting rates, degree of bit wear,
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Overall approximate Weight: Basic M
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Figure 5. 3 ft. diameter laboratory
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nozzle diameter and cutting speed w
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2. Cutting Speed The influence of c
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energy it effects an increase in me
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Tip angle (degrees) 87 Off-set angl
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Figure 5. Figure 6. Figure 7 Figure
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Figure 17. Figure 18. Figure 19. Fi
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SCHEMES OF COAL MASSIF BREAKAGE BY
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out thoroughly an efficient scheme
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Research analysis has proved that t
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DEPENDENCE OF POWER INDICES OF COMB
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The experiments have shown how the
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K Ay = coefficient correcting for f
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Figure 1. Schemes of combined break
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Figure 5. Dependence of specific en
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Figure 12. Percentage of grade R -6
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Figure 1. Particle size analysis. T
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NAME: Dr. Henkel COMPANY: Bergbau-F
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presented. This study, of course, i
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identifying a general trend for the
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Effect of Abrasive Hardness, Shape
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In some situations, especially in c
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Figure 1. Abrasive waterjet nozzles
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Figure 8. Effect of standoff distan
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Figure 13. Abrasive waterjet cuts i
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CUTTING WITH ABRASIVE WATERJETS M.
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3.3 Abrasive Feed Systems For abras
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Because of the large number of infl
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due to wear. Although actual operat
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from this new technology. Table 2 l
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Table 1. materials cut by abrasive
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Figure 1. Abrasive waterjet nozzles
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a) kerfs in mild steel b) S.S. 15.5
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a) circle cutting in glass b) lamin
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DISCUSSION NAME: Andrew F. Conn COM
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CUTTING HARD ROCK WITH ABRASIVE-ENT
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slurry nozzle. Testing at water pre
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DISCUSSION OF TEST RESULTS Jet Conf
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materials. The flexibility in nozzl
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pressure can be wiped out if diffic
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9. Maurer, W.C., and Heilheckler, J
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Figure 5. Effect of abrasive feed r
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Figure 9. Accumulated depth of mult
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Figure 13. Close-up view of quartzi
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ABRASIVE INJECTION USAGE IN THE UNI
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sudden changes in the feed rate eff
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or the abrasive must be manually to
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clog; there not being sufficient ar
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CODE OF PRACTICE FOR THE USE OF ABR
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Figure 5. Water abrasive cleaning h
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Figure 15. 360 0 abrasive pipe clea
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ECONOMIC CONSIDERATIONS IN WATER JE
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Other criteria to be considered in
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3 MANUAL METHODS OF JET CLEANING &
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contractor with old, unsafe, equipm
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Figure 1. Showing the increased cos
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Figure 8. Automatic tube bundle cle
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ackground to the subsequent coopera
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The molecules of SUPER-WATER posses
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shaken just before use. SUPERWATER
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26. Bednarz, L.P., "Effects of Poly
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