An experimental and numerical study of water jet cleaning process

Transcription

1 An experiental and nuerical study of water jet cleaning process Anirban Guha a,1,*, Ronald M. Barron a,b, Ra Balachandar c a Mechanical, Autootive & Materials Engineering Departent, University of Windsor Windsor, Ontario Canada N9B 3P4 b Departent of Matheatics & Statistics, University of Windsor Windsor, Ontario Canada N9B 3P4 c Civil and Environental Engineering Departent, University of Windsor Windsor, Ontario Canada N9B 3P4 * Corresponding author Tel: ; eail: [email protected] 1 Present Address: Civil Engineering Departent, The University of British Colubia, Vancouver, BC CanadaV6T 1Z4 ABSTRACT In this paper, we have experientally, nuerically and theoretically investigated the water jet cleaning process. Very high speed water jets (~ /s) are typically used in such cleaning operations. These jets diffuse in the surrounding atosphere by the process of air entrainent and this contributes to the spreading of the jet and subsequent decay of pressure. Estiation of this pressure decay and subsequent placeent of the cleaning object is of paraount iportance in anufacturing and aterial processing industries. Also, the pressure distribution on the cleaning surface needs to be assessed in order to understand and optiize the aterial reoval process. In an industrial setting, experiental study is perfored to forulate the pressure characteristics. It has shown that the decay of stagnation pressure along the axial direction is linear. It also revealed that no cleaning is possible at radial locations greater than 1.68D fro the centerline. Nuerical siulations are perfored to capture the process of air entrainent in the jet and the subsequent pressure characteristics. The siulation results are found to correctly predict the experiental data. Moreover, a theoretical odel for evaluating the optial and critical stand-off distances has also been derived. Based on our results, we found that the optial stand-off distance in cleaning operations is ~5D and the jet looses its cleaning ability at axial distances greater than ~26D. Keywords: CFD, Jet cleaning, Multiphase Flow, Nuerical Modeling, Water Jet PACS codes: Df; Ca; Wk; E-

2 1. Introduction High speed water jets in air are extensively used in anufacturing industry for cutting and cleaning operations. Water jets are used for reoval of various coatings or deposits fro the substrates and also for the cutting of any aterials. While water jet cutting involves the penetration of a solid aterial by a continuous jet, water jet cleaning involves an erosion process by which deposits are reoved fro the aterial surface. Hashish and duplessis (1978,1979) investigated the jet cutting process both analytically and experientally. They perfored a control volue analysis to evaluate the hydrodynaic forces. Later, their work was extended to find the optial stand-off distance. Siilar analysis was perfored by Leu et al. (1998) for the case of water jet cleaning. Cleaning water jets generally have the velocity range of ~ /s. They exhibit a high velocity coherent core surrounded by an annular cloud of water droplets oving in an entrained air strea. Leu et al. (1998) as well as Rajaratna et al. (1994, 1998) have discussed the anatoy of high speed water jets in air; see Figure 1. Such jets can be divided into three distinct regions: a) Potential Core Region: This region is the one close to the nozzle exit. In this region, priary as well as secondary Kelvin-Helholtz instabilities bring about transfer of ass and oentu between air and water. The process of air entrainent breaks up continuous water into droplets. There reains a wedge shaped potential core surrounded by a ixing layer in which the velocity is equal to the nozzle exit velocity. b) Main Region: The continuous interaction of water with surrounding air results in the break up of the water jet strea into droplets; the size of which decreases with the increase of radial distance fro the axis. Since the jet transfers oentu to the surrounding air, its ean velocity decreases and therefore it expands. The region closest to the jet-axis is known as the water droplet zone. There is another zone; viz. the water ist zone, which separates the droplet zone fro the surrounding air. This ist zone is characterized by drops of very sall size and negligible velocity. c) Diffused Droplet Region: This zone is produced by the coplete disintegration of the jet into very sall droplets having negligible velocity. Figure 1: Anatoy of high speed water jets in air

3 Rajaratna et al. (1994, 1998) did experients with a converging-straight nozzle having nozzle exit diaeter, D=2 and nozzle exit velocity (V o ) around 155 /s. They found that the centreline velocity of the jet reains constant and equal to V o for ore than 100D and then decays linearly to about 0.25 V o at about 2500D. Surprisingly; severe air entrainent causes the water volue fraction (α w ) to fall drastically. Measureents along the centreline show that α w at 20D is 20%, at 100D is 5% and at 200D, it is just 2%. Although they didn t perfor any pressure easureents, it is evident that such high degree of air entrainent will drastically decay the centreline pressure. The entrained air flows with the sae velocity as the water phase, but owing to the very low density of air in coparison to water (~1:815); the oentu delivered to the cutting or cleaning surface will be significantly reduced. Thus at oderately large stand-off distances (distance of the target surface fro the nozzle exit easured along the centreline), efficient cleaning will be ipossible. Research on nuerical siulations of high speed water jets has been very liited; and perhaps unsuccessful. Liu et al. (2004) tried to siulate the abrasive water jet (AWJ) cutting proble, but their results were not validated against experiental results. They used VOF ultiphase odel in FLUENT to siulate the two phase (water-air) flow but unfortunately, this odel (or any ultiphase odel) is not able to capture the air entrainent process. This is why the results of Liu et al. fail to siulate the actual flow physics as experientally observed by Rajaratna et al. (1994, 1998). It is worth entioning here that nuerical siulation of high speed jets faces significant challenges. Lin et al. (1998) concluded that the process of jet breakup and subsequent ist foration not only depends on the therodynaic states of both the liquid jet and the abient air but also has a strong dependence on the nozzle internal flow characteristics, e.g. nozzle cavitation, turbulence, etc. Yoon et al. (2004) did a series of experients with low, oderate and high speed jets. They inferred that the process of hydrodynaic instability and subsequent break-up echanis of high speed jets (Weber Nuber greater than 100,000) is significantly different fro the better understood Rayleigh type echaniss of the low/oderate speed jets. This infers that the theoretical understanding of echaniss related to high speed water jets is still not well developed. To bypass the theoretical liitations, Guha et al. (2010) developed a sei-epirical odel to capture the process of air entrainent. Based on epirical relations, this odel evaluates the interaction between air and water phases. This interaction ter is then incorporated into the governing Navier-Stokes equations as source ter. They validated their siulations against the experiental results of Rajaratna et al. (1994, 1998). The priary objective of this paper is to contribute to the knowledge of high speed jet ipingeent on a target plate and its effect on aterial reoval process. Before discussing any further, a brief introduction to the aterial reoval process is necessary. Jet ipingeent on the target coating creates ipact forces. The echanis of aterial reoval is very coplex. Adler (1979) proposed that aterial erosion by the water jets consist of four daage odes, viz. direct deforation, stress wave propagation, lateral outflow jetting, and hydraulic penetration. One or ore daage odes ay exist in a particular erosion process. Direct deforation and stress wave propagation are responsible for initiation of cracks. Watson et al.(1993) and Springer (1976) concluded that the propagation of stress waves caused by the ipact forces is generally responsible for crack initiation in the erosion process. Lateral outflow jetting and hydraulic penetration cause the extension, enlargeent and propagation of existing cracks. In the erosion of coating aterial, the adhesion between the coating and the substrate ay also need to be considered.

4 In order to have thorough understanding on the erosion process and thereby to produce an efficient cleaning, it is essential to have knowledge on the agnitude and distribution of the water jet pressure on the target plate. Leach et al. (1966) studied the pressure distribution on a target plate placed at a given axial distance fro the nozzle. They found that although the noralized pressure distribution along the centreline of a jet is dependent on the nozzle geoetry, it is independent along the radial direction. Their investigations showed that the jet pressure becoes equal to the abient pressure at a distance of around 1.3D fro the centreline. Outside this region, the shear stress is too sall to perfor cleaning of the target surface. They also found that the noralized pressure distribution was siilar for different inlet pressure conditions as well as different nozzle geoetries. In this paper, we have perfored experiental as well as nuerical studies to investigate the high speed water jet cleaning process. In an industrial setting, we have perfored experients to capture the centreline pressure as well as the radial distribution of pressure on the cleaning surface. For nuerical siulations, we have used the sei-epirical odel of Guha et al. (2010) to capture the air entrainent process. It is worthwhile to ention that previously the odel of Guha et al. has been ainly validated against the results of a free jet. Here we have extended the odel for the case of an ipinging jet. Thus, the odel has been thoroughly exained against our experiental results capturing the pressure characteristics on the target plate. Also we have used our experiental data to develop an epirical forula on the agnitude and distribution of pressure on the target plate at a given stand-off distance. Apart fro that, we have ade a brief contribution to the theoretical aspect of water jet ipingeent by deriving forulas for optial and critical stand-off distances. 2. Sei-Epirical ass-flux odel The sei-epirical ass flux odel of Guha et al. (2010) cobines analytical and epirical ethods to evaluate the ass flux at a particular location (x, r) inside the jet. It is expressed as follows: V R r M& ρ ( x, r) = w α wo wo N 1 2 (1) R R 3 Here, M & ( x, r) is the ass flux of water droplets at the location (x, r), ρ w is the density of water, α wo and V wo are the volue fraction and axial velocity of water droplets at the nozzle exit respectively, R N is the nozzle radius. The variable R is defined as R = R i if r Ri, R= R o if Ri < r Ro (2)

5 Where R i is the radial width of the continuous flow region and is given by R k xr + R i = 1 (3) Outside of this region is the droplet flow region, the radial width of which varies as N o R N N R = Cx + (4) k 1 and C are Spread Coefficients. The value of C is usually in between 0.02 and k 1 is estiated as follows: k RN = const C 1 (5) where const is usually O(10-1 ). Scheatic description of R i and R o has been provided in Figure 1. In Equation (1), α wo is usually 1.0. Hence, if the nozzle exit velocity and the Spread Coefficients are known, the jet flow characteristics can be properly estiated. 3. Nuerical Siulation Here we adopt the nuerical ethodology undertaken by Guha et al. (2010). In order to ipleent Equation (1) nuerically, it is coupled with the continuity and oentu equations of turbulent ultiphase flows Governing Equations and Solution Methodology The governing equations of this proble are Navier-Stokes equations for turbulent ultiphase flows. The ultiphase odel chosen for this proble is the Eulerian ultiphase odel. k-ε turbulence odel with standard wall functions are used to capture turbulence. The continuity and oentu equations for the w (water) phase in the Eulerian odel for ultiphase flows are, respectively ( α w ρ w ) + t r (α wρ wvw ) + α t r ( α w ρ wv w ) = ( & a w & w a ) + S w i= w, a ( ρ v v ) = α p + τ + α ρ g + w w r w r w w w w w v (6)

6 The ter w a i= w, a r r r r r ( (7) { K wa vw va ) + & a wva w & w avw a } + Fw & is the ass transfer fro w (water) phase to a (air) phase. In order to siulate the air entrainent process, we set & a w where M & is known fro Equation (1). & and S w as zero and w (M& a =,0) (8) FLUENT is used as the flow solver. Water is treated as the secondary phase. The drag coefficient between the two phases is deterined by the Schiller-Nauann equation (Fluent User Manual). Equation (8) is incorporated into FLUENT by the eans of User Defined Functions r (UDF). The source ter due to oentu transfer ( & v ) in Equation (7) is autoatically handled by FLUENT once the ass transfer is specified (through UDF). This is done as follows: w a w a r r v w = v a a if w a & > 0, r r v w a = v w if & w a < 0 (9) The ter K wa ( v r r w va ) in Equation (7) represents inter-phase interaction force and K is the wa inter-phase oentu exchange coefficient. The k-ε ixture turbulence odel is used for turbulence odeling. The transport equations are as follows: ( ρk) r + t ( ρ ε ) + t µ σ k t, ( ρ kv ) = k + G ρ ε µ σ k, t, ( ρ εv ) = ε + ( C G C ρ ε ) r ε ε k 1ε k, 2ε (10) (11) where ρ is the ixture density and v r is the ixture velocity. The turbulent viscosity ( µ t, ) and the production of turbulent kinetic energy (G k, ) are calculated as follows: 2 ρ C k t, = (12) ε µ µ G k, t, r r T ( v + ( v ) ) = µ (13)

7 The values of the odel constants are taken as the standard values C 1ε = 1.44, C 2ε = 1.92, C µ = 0.09, σ k = 1.0, σ ε = 1.3. Standard wall functions are used to odel near wall flows. For brevity, the description of standard wall functions is not discussed. Interested readers can refer to FLUENT User Manual for details Coputational Doain and Boundary Conditions Following Guha et al. (2010), the coputational doain (see Figure 2) and structured grid syste is created in GAMBIT. In all our probles, we have dealt with circular jets. Hence the doain is ade two diensional and axisyetric (half of the doain was siulated). The boundary conditions appear as shown in Figure 2. The radial extent of the doain is large enough to ensure that the pressure outlet boundary condition (set at atospheric pressure) and the wall boundary conditions can be accurately applied, i.e., without adversely affecting the flow field. It is iportant to note that we have used a wall boundary condition near the velocity inlet. Replacing it with the ore realistic pressure outlet boundary condition ay cause backflow of the jet. Also, the use of internal boundary condition helps in dividing the doain into two parts, the one inside the jet region with densely clustered grids which the other one with variable grid spacing, the size of which increases towards the pressure outlet boundary. The velocity inlet condition can be obtained by solving the nozzle flow proble separately provided the nozzle geoetry and nozzle inlet conditions are known. The nozzle exit velocity profile will then becoe the velocity inlet condition for the jet flow proble. In all the probles considered in this paper, the nozzle exit velocity is fully developed and turbulent, and the nozzle is assued to be frictionless. Hence the nozzle exit velocity has top-hat profile. Firstly, we have tried to siulate the flow conditions given in Rajaratna et al. (1994, 1998). We have ade the doain size to ensure that the boundaries are far apart fro the jet. Rajaratna et al. studied free jet proble, hence the wall boundary at the opposite end of the velocity inlet is not iportant for this particular proble. The radial width (R N ) of the velocity inlet boundary (set at 155 /s) is 1 as per the experiental conditions. Figure 2: Coputational doain and boundary conditions (Not drawn to scale)

8 In validating other experiental results, we use the sae coputational doain as shown in Figure 2, but the geoetry is different and proble specific. The sae is true for boundary conditions. These will be discussed in details in the relevant sections of the paper. The initialization of the probles can be done by setting the water phase volue fraction equal to 1 at the velocity inlet and 0 elsewhere. The proble with this approach is that it will take very long tie to perfor the coputations. To bypass this proble, we take the help of internal boundary condition shown in Figure 2. We ake the water phase volue fraction inside the entire region within the internal boundary and the axis to be 1. The sae is set to 0 in the other half of the doain. Since the jet will eventually reach the wall and we are interested in the steady state behavior of the proble, this initialization trick helps to save considerable aount of coputational tie. In all the probles, pressure-velocity coupling is achieved using the phase-coupled SIMPLE algorith. All the residuals tolerances are set to 10-6 and the tie step size is 10-5 seconds. The progra is run for a tie long enough to attain quasi-steady state. 4. Validation of Nuerical Results Like Guha et al. (2010), we have validated the published experiental results of of Rajaratna et al. (1994, 1998) and Leach et al. (1966). Figures 3-4 copare the siulation results with that of Rajaratna et al.. Indeed Rajaratna et al. found that the centreline velocity (V o ) of the jet reains constant for ore than 100D and then decays linearly to about 0.25V o at about 2500D. Severe air entrainent causes the water volue fraction (α w ) to fall drastically fro 20% at 20D to 5% at 100D. Figures 3-4 confir that the siulation accurately predicts the centreline characteristics. The User Defined Function added to the FLUENT solver for the validation of these results has been provided in the Appendix. It is iportant to ention here that the radial velocity distribution (not included in study, but for reference see Guha et al. (2010)) deviates fro the experiental findings of Rajaratna et al. (1994) for radial width greater than 5D. At such distances, the water ist zone is ore proinent. Since the ist zone is fored of sparse droplets, the continuu hypothesis becoes invalid; hence, the odel is no longer suitable to capture the flow physics. Note that the ist zone has alost no effect in cleaning applications; hence its odeling is not a ajor concern. Fro cleaning point of view, the pressure distribution on a target plate (P T ) placed perpendicularly to the jet flow field is of priary concern. Since the jet looses sufficient aount of centreline pressure (P T (x,0)) as it progresses through the surroundings, to ensure efficient cutting or cleaning, the target plate should be kept near the nozzle exit. It is essential for the siulation to predict the pressure distribution at the target plate fairly accurately. Fro the previous paragraph, we cae to know that the odel of Guha et al. gives a good prediction of the characteristics of a free jet. Hence it has been extended to understand the pressure characteristics of an ipinging jet. Thus, the experiental conditions (jet velocity of 350 /s, nozzle radius of 0.5 and stand-off distance 76 ) of Leach et al. (1966) has been

9 nuerically ipleented. Here the doain is ade to properly satisfy the geoetry and boundary conditions. Care should be taken while perforing the siulations with ipinging jets. Near the zone of ipingeent, the jet dynaics changes considerably and the ass flux odel no longer holds. This is because the ass flux odel is based on free jets. To tackle this proble, the axial length of the jet along which the ass flux relation holds is prescribed to be a little less than that of the axial length of the doain (to be on the safe side, we kept it to be a few illieters less than the point where stagnation took place). Figure 5 shows the coparison between the siulation results and the experient. It sees that the nuerical siulation under predicts the experiental data. The reason behind this deviation will be discussed in Section 5. Fro the validations discussed above, it is evident that the ass flux odel gives reasonable predictions of both the axial (centreline) as well as the radial characteristics.. Figure 3: Nuerical siulation of the decay of centreline water phase volue fraction and coparison with experiental results of Rajaratna and Albers (1998).

10 Figure 4: Nuerical siulation of noralized centreline water phase velocity and coparison with experiental results of Rajaratna et al. (1994). Figure 5: Noralized pressure distribution on a target plate placed at 76D and coparison with Leach et al. (1966).

11 5. Experiental Set-up As has been already discussed, there has been soe experiental works on cleaning jets. Yet, there is no consuate view on the agnitude and distribution of water pressure on the target plate. Without this knowledge, it is not possible to design an efficient cleaning syste. This has otivated us to perfor experiental investigations on the pressure distribution on the target plate. A scheatic of the experiental setup is illustrated in Figure 6. The capacity of the pup was /s and 5 MPa. The converging nozzle used in this study is long, with largest diaeter and sallest diaeter (D) The pressure reducing valve ounted on the line feeding water fro the pup to the nozzle is able to reduce the pressure to 1.03 MPa. The static pressure at the nozzle inlet is easured with the aid of a pressure transducer. The ass flow rate of water through the nozzle is easured using a collecting vessel and stop-watch. Since the nozzle geoetry and ass flow rate are known, the average velocity at the nozzle exit can be easily deterined. The water, flowing out of the nozzle in the for of a high speed jet, ipacted onto a target, which can be oved both axially and radially with the aid of a robotic ar. The Figure 6: Scheatic of the experiental set-up and the nozzle geoetry. Labels : (1) Pup 5 MPa, /s (2) Pressure Reducing Valve - up to 1.03 MPa (3) Pressure Transducer 0 to 6.9 MPa, 0 to 5 V (4) Converging Nozzle (5) Target Plate (6) Pressure Transducer 0 to 13.8 MPa, to V, V/MPa (7) Linear Variable Displaceent Transducer ±0.381, 0-5 V, /V (8) A/D Converter with 8 channels (9) Coputer

12 Figure 7: High speed water jet for cleaning operations. target plate has a pressure transducer (Uncertainty =2%) ounted at its centre. The distance oved by the target in both axial and radial directions is easured by a Linear Variable Displaceent Transducer (Uncertainty =0.5%). The signals obtained by the sensors (sapling frequency = 1 KHz) are acquired by a data acquisition syste and subsequently analyzed in a coputer. Figure 7 shows the jet eanating fro the nozzle during the experients. Table 1 lists the different test cases considered in this experient. For all the cases, the target plate is oved along the centreline with the aid of a robotic ar fro to fro the nozzle exit. Test Case Nozzle Inlet Pressure (P N ) Mass flow rate (M & ) Nozzle exit velocity (V o ) Spread Coefficient (C) MPa Kg/s /s Table 1: Different experiental test cases

13 The starting point is kept at fro the nozzle exit in order to ensure that the ain strea jet flow does not get obstructed by the rebounding flow fro the target plate. Also within 0.085, it is very difficult to take correct easureents of the Spread Coefficient, C. In fact, the rebounding flow can cause daage to the pup and accessories. The velocity of the robotic ar is 0.01 /sec and thus the relative otion between the jet and the robotic ar is negligible. The target pressure and axial displaceent data are recorded during this operation. In this way, the distribution of pressure along the centreline of the jet is obtained. In the next step, the target plate is kept at a fixed axial distance of fro the nozzle exit and is oved radially. The target pressure and radial displaceent data were recorded during this operation. The Spread Coefficients (C) of the jets for different test cases are obtained with the help of a scale (1 resolution) and photographs captured by a Nikon D300 caera. The forer is defined as the ratio of difference between the radial width of the jet at the location of the scale and the nozzle exit radius (R N ) to the axial distance between the scale and the nozzle exit. Once C is known, k 1 can be estiated using Equation 5. The centreline pressure on the target plate, P T (x,0) (which is the stagnation pressure) is found to vary linearly with the axial distance. On noralizing the target pressure by total pressure at the nozzle inlet (P N ) and noralizing the axial distance by nozzle exit diaeter (D = ), it is found that all the pressure curves collapse onto one curve. This is shown in Figure 8. This linear relation can be expressed as Figure 8: Noralized stagnation pressure on the target plate.

14 P T P x D N,0 = x D + P P E N (14) where is the slope, and is under the experiental conditions. P E is the pressure at the nozzle exit. In industrial cleaning nozzles, the losses inside the nozzle due to friction is negligible, hence the rightost ter in the right hand side is alost equal to 1. It is worth entioning that this linear relationship holds for distances at least within ~50D. In the next experient, the target plate is kept at a fixed stand-off distance of fro the nozzle exit and is oved radially. Figure 9 shows the radial distribution of target pressure for all the three cases, after noralizing the pressure (P T ) by the corresponding pressure on the jet axis (P T (x/d,0)) and radial distance by nozzle exit diaeter. The noralized distributions for these test cases are self siilar and can be expressed by the following Gaussian distribution: x r PT, D D x PT,0 D = exp r D 2 (15) The radial position (R Pat ) corresponding to the value zero of the Gaussian curve fit is the position where the pressure on the target plate is equal to the atospheric pressure. The value of R Pat is found to be 1.68D. The deviation with the experiental results of Leach et al. (1966) is clearly visible. They predicted R Pat to be 1.3D. The difference with our result is because their prediction was based on an analytical curve which is a third order polynoial satisfying the boundary conditions of the given proble. Our Gaussian curve fit has an R-squared value ~ This is the reason why our nuerical results in Figure 5 deviated fro the experiental results of Leach et al. (1966). It is interesting to note that the value of R Pat is invariant with the axial position of the target plate. Exaining Equation (15) we observe that the exponential part which represents the distribution of the pressure on the target plate is only dependent upon the radial coordinate. Thus, although the jet spreads in air and its radial width increases, the radial location where the target pressure turns atospheric (R Pat ) reains fixed at the value of 1.68D (See Figure 10). Figure 10 shows the scheatic of the pressure distribution on the target plate at two different locations, Location 1 being nearer to the nozzle. The pressure is axiu at the centreline and its distribution is Gaussian in the radial direction. As the jet progresses, it transfers oentu to the surroundings and thus continues to spread. This results in not only a reduced peak pressure (stagnation pressure) at the target plate, but also a decrease in overall pressure distribution.

15 Cobining Equations 14 and 15, the overall pressure characteristics at the target plate can be represented as follows exp, + = D r P P D x P D r D x P N E N T (16) Figure 9: Experiental noralized target pressure along the radial direction and its coparison with Leach et al. (1966). Figure 10: Scheatic of the pressure distribution on the target plate.

16 In Springer (1976), investigation of the repetitive ipacts of ultiple liquid droplets on a solid surface was perfored. They proposed that aterial reoval occurs due to fatigue at a certain nuber of stress cycles when the equivalent dynaic stress is between the ultiate strength and the endurance liit of the aterial. Material reoval ceases to occur if the equivalent dynaic stress is saller than the aterial's endurance liit. This can be atheatically represented as follows: M & λψ S (17) Here λ, ψ and S are the stress coefficient (depending on the droplet size, coating thickness, and properties of the liquid, coating, and substrate aterial), speed of sound in liquid and endurance liit respectively. Based on this theory, Leu et al. (1998) proposed a critical stand-off distance, x c (shortest stand-off distance at which no cleaning is possible) and its relation with the optial stand-off distance, x (stand-off distance providing axiu cleaning). It occurs when the following condition is satisfied: M & ( x,0)λψ = S (18) Fro that they found the following relations: x c λψk = 2.82 S 0.5 R C N PN ρ w (19) x = (20) x c Here k is the flow resistance coefficient and is ~ Although their derivation ethodology was right, we have noted a vital shortcoing of this approach.. They derived Equations (19) and (20) based on Equation (4). Evaluation of critical or optial stand-off distance should be based on Equation (3) rather than Equation (4). This is because stand-off distance is evaluated along the centreline, hence Equation (3), which deals with the inner region of the jet is the appropriate one. Incorporating this change and proceeding uch like Leu et al., the new forula for critical stand-off distance is found to be: x c R = k N ρ w0vw0λψ 1 S 2 (21)

17 Also, we are able to obtain a relation between the critical and optial stand-off distances which is as follows: x x = R N c (22) k1 If the Right hand side of Equation (22) is sall, it can be approxiated to be zero. In that case, x (23) x c As pointed out in Leu et al. (1998), it is extreely difficult to evaluate λ, hence these theoretical relations are not practically helpful in evaluating x c or x. Also, we found (see Figure 8) that x (or x /D) cannot be easured experientally because keeping the target plate too close to the nozzle exit produces flow reversal. Fortunately, our nuerical siulations have given accurate predictions of jet characteristics; hence it can be applied to evaluate x. 6. Nuerical Siulation Corresponding to the experiental results obtained in Section 5, nuerical siulations are perfored. Since we didn t perfor any velocity easureents, the velocity profile at the nozzle exit is not known to us. We have easured the ass flow rate and fro that we calculated the average velocity at the nozzle exit. Since the nozzle inlet pressure is known and the nozzle outlet pressure is atospheric, we can use these paraeters as well as the ass flow rate to nuerically siulate the flow features inside the nozzle. For our nozzle geoetry, we have found that the flow inside the nozzle becoes fully developed turbulent flow. Under the assuptions that the turbulence intensity at the nozzle inlet is 10% and the nozzle is frictionless, we obtained the nozzle exit velocity to be of top-hat profile. Figure 11 shows the velocity and turbulence intensity distribution in the nozzle for the Test Case 2 (the corresponding siulation is naed Si 2). This nozzle exit velocity and turbulence profile is used as the boundary condition for the jet flow proble. The doain is ade The boundary conditions and other relevant paraeters are already known fro the experiental conditions. The ethodology of creating the doain, setting up the CFD solver and incorporation of the sei-epirical ass flux odel in FLUENT is the sae as that discussed in Section 3.

18 (a) (b) Figure 11: (a) Velocity distribution and (b) Turbulence Intensity distribution inside the nozzle corresponding to Test Case 2 (i.e. Si 2). (a) (b) Figure 12: (a) Velocity and (b) Volue fraction of water phase of the jet corresponding to Test Case 1 (i.e. Si 1). Figure 12 shows the velocity and volue fraction contours for Si 1. The contour plot shows the behavior of the jet after it eanates fro the nozzle (the axiu axial distance shown in the figure is 5D). Several qualitative inferences can be drawn fro Figure 12, viz. (i) the velocity profile is top-hat, (ii) there are undulations on the velocity profile which clearly show the growth of instability in the shear layer as one would expect, (iii) the jet expands alost linearly, (iv) a strong shear layer is concentrated at the jet boundary and (v) considerable aount of air is entrained within the jet and the water phase volue fraction is axiu at the centerline and decreases rapidly with radius. Although the results here are for Si 1, exactly siilar behavior is observed in the other siulation cases.

19 Figure 13 (a) and (b) respectively shows the water phase velocity and volue fraction distributions in the radial direction for three different axial distances. The case considered here is Si 1. As has already been discussed, the velocity distribution reains top hat even at 30D ainly due to the sharp density interface (~1:815) between air and water. The volue fraction distribution shows a kind of Gaussian profile with a bulge. Since the ist region is not included in the nuerical odeling, the volue fraction of water actually lost as ist nuerically accuulates near the jet-air interface and produces the erroneous bulging effect. The bulging effect flattens out with increased axial distance. It is seen that the volue fraction decreases rapidly with increased axial distance while the velocity reains fairly constant. Also the volue fraction profile is thinner than the velocity profile. All these observations are in congruence with the experiental findings of Rajaratna et al. (1998). Figure 14 shows the coparison between the experiental and nuerical results of the pressure distribution on the target plate for the three test cases. The stand-off distance is kept constant at (x/d = 43.03). The difference between the experiental and nuerical results is priarily due to the uncertainty in easuring C, which is ~7-8%. In order to find the optial stand-off distance, a set of siulations are perfored by oving the target plate boundary. It is found that the stagnation pressure (P T (x,0)) is axiu at x=5d, and there is no backward flow (in case of backward flow, the solution diverges). This is intuitively right, since ~5D arks the end of the potential core. Thus, on the basis on Equation (22) and our experiental paraeters, the optial and critical stand-off distances can be suarized as follows: x = 5D, x c 26D = (24) (a) (b) Figure 13: (a) Water phase velocity and (b) Volue Fractions at x/d=10, 20 and 30 corresponding to Si 1.

20 Figure 14: Coparison of experiental (denoted by Case ) and corresponding siulation (denoted by Si ) results for target pressure 7. Conclusion Both experiental study and nuerical siulations are perfored to understand the behavior of cleaning jets. These jets diffuse in the surrounding atosphere by the process of ass and oentu transfer. Air is entrained into the jet strea and the whole process contributes to the spreading of the jet and subsequent decay of pressure. The agnitude and distribution of pressure on the cleaning surface (target plate) has been obtained using both experiental and nuerical ethods. A sei-epirical ethod has been ipleented in the nuerical siulation to capture the air entrainent process properly. The nuerical results are validated against the experiental results available in literature as well as our own experients. Also, a theoretical odel to calculate the critical and optial stand-off distances has been proposed. Based on our nuerical results, we have concluded that the optial stand-off distance is ~5D fro the nozzle exit, and the jet looses its cleaning ability at ~26D (critical stand-off distance). Keeping the target plate too close to the nozzle causes the jet to rebound fro the cleaning surface and obstruct the nozzle flow, thereby decreasing cleaning efficiency. On the other hand, if the surface is kept too far fro the nozzle, the jet will transfer oentu to the surroundings, thereby producing huge pressure loss and thus inefficient cleaning. The latter is a direct consequence of the excessive water phase volue fraction decay (Figure 3). Fro our experiental findings, we have found that the cleaning radius (R Pat ) of the jet is 1.68D. Thus, debris located at a radial distance greater than 1.68D is definitely irreovable by the cleaning jets. Our proposed siulation ethodology can be helpful for predicting the flow behavior of jets used in industrial cleaning applications since these applications focus on the near-field region of the jet. The siulation correctly predicts the agnitude and distribution of pressure on the

21 cleaning surface. The knowledge of nozzle inlet conditions and the Spread Coefficient are required as paraeters for the siulation, and these paraeters can be obtained without uch difficulty. The experiental and nuerical results on pressure distribution on the target plate will help the understanding of the erosion process and subsequent aterial deforation. Finally, it is worth entioning that the experiental and nuerical ethodologies can be extended to water jet cutting operations. Acknowledgeent We would like to thank Valiant Machine and Tool Inc., Windsor, Ontario, Canada for providing us experiental support. References Adler, W. F., The Mechaniss of Liquid Ipact. Treatise on Materials Science and Technology, Acadeic Press. FLUENT User Manual Guha, A., Barron, R. M., and Balachandar, R., Nuerical Siulation of High Speed Turbulent Water Jets in Air. Journal of Hydraulic Research, 48(1), Hashish, M., and duplessis, M. P., Theoretical and Experiental Investigation of Continuous Jet Penetration of Solid. ASME Journal of Engineering for Industry, 100, Hashish, M., and duplessis, M. P., Prediction Equations Relating High Velocity Jet Cutting Perforance to Standoff Distance and Multipasses. ASME Journal of Engineering for Industry, 101, Leach, S. J., Walker, G. L., Sith, A. V., Farer, I. W., Taylor, G., Soe Aspects of Rock Cutting by High Speed Water Jets. Philosophical Transactions of the Royal Society of London, 260 (1110), Leu, M.C., Meng, P., Geskin, E.S., Tiseneskiy, L., Matheatical Modeling and Experiental Verification of Stationary Water Jet Cleaning Process. Journal of Manufacturing Science and Engineering, 120(3), Lin, S.P., Reitz, R.D., Drop and Spray Foration fro a Liquid Jet, Annual Review of Fluid Mechanics, 30,

22 Liu, H.,Wang, J.,Kelson, N.,Brown, R.J., A study of abrasive waterjet characteristics by CFD siulation. Journal of Materials Processing Technology, , Rajaratna, N., Steffler, P.M., Rizvi, S.A.H., Sy, P.R., Experiental Study of Very High Velocity Circular Water Jets in Air. Journal of Hydraulic Research, 32(3), Rajaratna, N., Albers,C., Water Distribution in Very High Velocity Water Jets in Air. Journal of Hydraulic Engineering, 124(6), Springer, G. S., Erosion by Liquid Ipact. Scripta Publishing Co., Washington, DC. Watson, J. D., Theral Spray Reoval with Ultrahigh-Velocity Waterjets, Proceedings of 7th Aerican Waterjet Conference, Seattle, WA, pp Yoon, S.S., Hewson, J.C., DesJardin, P.E., Glaze, D.J., Black, A.R., Skaggs, R.R., Nuerical Modeling and Experiental Measureents of a High Speed Solid-Cone Water Spray for Use in Fire Suppression Applications, International Journal of Multiphase Flow, 30, Appendix The User Defined Progra (UDF) used to validate the experiental results of Rajaratna et al. (1994, 1998) is as follows: #include "udf.h" #include "threads.h" #include "etric.h" #include "e.h" #include "sg_phase.h" DEFINE_MASS_TRANSFER(watertoair,cell,t,fro_index,fro_species_index,to_index,to_spe cies_index) { /* variable declarations*/ real _lg1; real x[nd_nd]; double Ro,Ri,rad; real rn=0.001; /*radius of nozzle=1*/ real v0=155;/*input velocity*/

23 real terro,terri; double dmdrro,dmdrri,dmdro1,dmdro2,dmdro,dmdri1,dmdri2,dmdri,drodx,dridx; real const1=v0*rn*rn*5.62*998.2;/*alpha rho vel rn rn 5.62 */ _lg1=0; /*ass transfer ter as reconginzed by FLUENT */ C_CENTROID(x,cell,t); Ro=0.05*x[0]+ rn;/*ro is the width in the outer region.. Eq 4*/ Ri=0.65*sqrt(rN*x[0])+rN;/*Ri is the width in the inner region.. Eq 3*/ rad=x[1]; /*radial coordinate*/ /* defining the ass flow rate derivatives in the two regions */ dmdrro=4.5*const1*pow((1-pow(rad/ro,1.5)),2)*pow(rad/ro,0.5)*(1/(ro*ro*ro)); dmdrri=4.5*const1*pow((1-pow(rad/ri,1.5)),2)*pow(rad/ri,0.5)*(1/(ri*ri*ri)); dmdro1=4.5*const1*rad*pow((1-pow(rad/ro,1.5)),2)*pow(rad/ro,0.5)*(1/(ro*ro*ro*ro)); dmdro2=-2*const1*pow((1-pow(rad/ro,1.5)),3)/(ro*ro*ro); dmdro=dmdro1+dmdro2; dmdri1=4.5*const1*rad*pow((1-pow(rad/ri,1.5)),2)*pow(rad/ri,0.5)*(1/(ri*ri*ri*ri)); dmdri2=-2*const1*pow((1-pow(rad/ri,1.5)),3)/(ri*ri*ri); dmdri=dmdri1+dmdri2; drodx=0.05;/* derivative of Eq 4 wrt x*/ dridx=0.325*rn/sqrt(rn*x[0]);/* derivative of Eq 3 wrt x*/ terro=dmdrro+dmdro*drodx; terri=dmdrri+dmdri*dridx; if(rad<=ri) /*if within the inner region of the jet.. Eq 2 */ {_lg1=terri/4000;} /*..the nuber 1/4000 coes fro the cell di */ if((rad<=ro)&&(rad>ri)) /*if within the outer region of the jet.. Eq 2*/ {_lg1=terro/4000;} if(rad>ro) /*neglect ass transfer in ist region*/ {_lg1=0;}

24 return _lg1; } List of Tables Table 1: Different experiental test cases List of Figures Figure 1: Anatoy of high speed water jets in air (Leu et al. (1998)) Figure 2: Coputational doain and boundary conditions (Not drawn to scale) Figure 3: Nuerical siulation of the decay of centreline water phase volue fraction and coparison with experiental results of Rajaratna and Albers (1998). Figure 4: Nuerical siulation of noralized centreline water phase velocity and coparison with experiental results of Rajaratna et al. (1994). Figure 5: Noralized pressure distribution on a target plate placed at 76D and coparison with Leach et al. (1966). Figure 6: Scheatic of the experiental set-up and the nozzle geoetry. Labels : (1) Pup 5 MPa, /s (2) Pressure Reducing Valve - up to 1.03 MPa (3) Pressure Transducer 0 to 6.9 MPa, 0 to 5 V (4) Converging Nozzle (5) Target Plate (6) Pressure Transducer 0 to 13.8 MPa, to V, V/MPa (7) Linear Variable Displaceent Transducer ±0.381, 0-5 V, /V (8) A/D Converter with 8 channels (9) Coputer Figure 7: High speed water jet for cleaning operations. Figure 8: Noralized stagnation pressure on the target plate. Figure 9: Experiental noralized target pressure along the radial direction and its coparison with Leach et al. (1966). Figure 10: Scheatic of the pressure distribution on the target plate. Figure 11: (a) Velocity distribution and (b) Turbulence Intensity distribution inside the nozzle corresponding to Test Case 2 (i.e. Si 2). Figure 12: (a) Velocity and (b) Volue fraction of water phase of the jet corresponding to Test Case 1 (i.e. Si 1).

25 Figure 13: (a) Water phase velocity and (b) Volue Fractions at x/d=10, 20 and 30 corresponding to Si 1. Figure 14: Coparison of experiental (denoted by Case ) and corresponding siulation (denoted by Si ) results for target pressure