SECTION 6 FLUIDS ENGINEERING. ASME 2012 Early Career Technical Journal - Vol

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1 SECTION 6 FLUIDS ENGINEERING ASME 212 Early Career Technical Journal - Vol

2 ASME 212 Early Career Technical Journal - Vol

3 ASME Early Career Technical Journal 212 ASME Early Career Technical Conerence, ASME ECTC November 2 3, Atlanta, Georgia USA MIXING TIME DETERMINATION OF STEADY AND PULSE JET MIXERS Ibraheem R. Muhammad and John P. Kizito Department o Mechanical Engineering North Carolina A&T State University Greensboro, NC, USA ABSTRACT The present study ocuses on the perormance o continuous and pulsing jet mixers by experimental and computational luid dynamics (CFD). Pulse jet mixers have not been studied extensively and it is necessary to provide urther insight into the perormance o pulse jet mixers compared to steady jet mixers. A jet pulse is created by turning the inlet jet velocity on and o in a cyclic manner. The mixing time and low patterns o dierent conigurations o jet mixers are studied or single and multiple jet conigurations. Experimentally, the low patterns and mixing time are studied using a dye tracer. The concentration at the outlet o the mixing time is measured using a spectrophotometer. CFD methods are used to visualize the low patterns created in the tank as well. Results show that the mixing time decreases as the jet Reynolds number increases and increases the momentum lux entering the mixing tank. Mixing time is aected by the orientation o the jets and the ability o the jet to recirculate o the walls, which can also eliminate low mixing zones. As a ree jet turns into a wall jet, mixing is diminished. The current results give some insight into the potential or pulse jet mixers or mixing in various processes. NOMENCLATURE C Concentration (g/ml) o dye tracer at time, t C o Initial concentration (g/ml) o dye tracer C Final concentration (g/ml) o dye tracer C p Heat capacity (J/kg K) D Tank diameter (m) D nozzle Jet nozzle diameter (m) D ov Overlow port diameter (m) D pipe Pipe outside diameter (m) DC Duty cycle (DC = t D/ t C ) g Gravity acceleration constant (m/s 2 ) H Tank height (m) H luid Liquid level height (m) k Thermal conductivity (W/(m K) L Characteristic length scale (m) m Mixing time parameter P Pressure (Pa) Pe Peclet number (Pe = ρ L V/k C p ) Q Jet volumetric low rate (m 3 /s) Re j t t C t D T T M * T M V Jet Reynolds number (Re j = V D nozzle /υ) Time (s) Pulse cycle time (s) Jet discharge time (s) Temperature (K) Mixing time (s) * Dimensionless mixing time (T M = T M /(D 2 /(Q V) 1/2 ) Jet velocity (m/s) Greek symbols λ max Maximum wavelength (nm) µ Dynamic viscosity (N s/m 2 ) υ Kinematic viscosity (m 2 /s) ρ Liquid density (kg/m 3 ) INTRODUCTION Jet mixers are common mixing devices used in numerous processes. They are used in liquid blending, solid suspension, and gas/liquid contacting [1], chemical reactions [2, 3], storage tank homogenization [4], controlling process parameters and reducing thermal stratiication [5], and nuclear waste processing [6]. Jet mixers operate by withdrawing luid rom the mixing tank and supplying the luid back to the tank through a nozzle at high velocities. As the jet is discharged, it expands and the relative velocity between the jet and the bulk luid causes the bulk luid to get entrained by the jet. They are advantageous compared to other mixing devices as they have the ability to provide adequate mixing, high turbulence and shear rates, while operating with no moving parts and easy installation. Quantitative and qualitative measurement o mixing is important in mixing processes. The most common parameter to estimate the mixing perormance o jet mixers is mixing time, or blend time. Patwardhan and Gaikwad [3] has summarized mixing time correlations that have been developed or past jet mixing studies. Most o the correlations have been developed using dierent measurement techniques and are only applicable to a limited range o parameters. Jet mixing has been studied experimentally [7-14] and by computational luid dynamics (CFD) [15-2] by many researchers. Mixing time is usually measured experimentally by monitoring a scalar quantity o some tracer (dye, electrolyte, hot water) as a unction o time. The mixing time is measured ASME 212 Early Career Technical Journal - Vol

4 as the time it takes or the tracer to reach a certain amount o homogeneity in the vessel, usually 9 or 95%. In the past decade, several CFD studies on jet mixing have been completed which ocuses on the actual low patterns created in mixing vessels [17, 19, 21, 22]. All the studies have been run using dierent jet mixer conigurations, but some general results have been ound. The jets create circulatory patterns in the tank as they interact with the walls o the tanks. Dierent patterns have been noticed depending on the shape o the tank, length o the jet, jet angle, and number o jets. However, there have not been many studies that ocus on pulsing jet mixers. Pulsing, or pulse, jet mixers are mainly used or nuclear waste remediation in which pulsing is created using compressed air to vent and discharge contents within a tank. Pulsing jets have been ound to increase entrainment close to the jet due to increased vortices [23, 24]. Zhang and Johari [23] studied accelerating jets and ound that there was a decrease in entrainment rate due to the acceleration. Anders et al. [25] used large eddy simulations (LES) and Reynolds-averaged Navier- Stokes (RANS) simulations to study the interaction between an initial pulse ollowed by a subsequent pulse. Results o LES simulations showed that there was a reduced strength o the vortex head rom the irst pulse. The results o the RANS simulations showed that the turbulent kinetic energy o the second pulse decreased due to the irst pulse. Ranade [21] studied alternating jet sequences and noticed that though there is not an overall increase in mixing, initial dispersion o a tracer is enhanced. Muhammad and Kizito [15] studied mixing time or dierent number o jets or both continuous and pulsing jet mixers. It was shown that mixing times or pulsing jets and continuous jets are similar. However, pulsing jets can provide increased local vortices and be useul or mixing in certain applications. The current study ocuses on the mixing perormance o jet mixers using both experimental and CFD techniques. The mixing time and low patterns or continuous and pulsing, single and multiple jet mixer conigurations are experimentally studied. A dye is used to calculate mixing time experimentally and imaging techniques are used to observe low patterns. Flow patterns are urther visualized using CFD. The results can be used as tools or application to a variety o processes, including liquid blending and solid suspension. EXPERIMENTAL METHODS Figure 1 shows a schematic o the jet mixing system used in the current study. The driving orce or the jet is a centriugal pump, which suctions luid rom a holding tank. Figure 2 displays the actual jet mixing system used or experimental studies. The jet mixing apparatus included a cylindrical, polycarbonate tank (D =.35 m and H =.61 m) enclosed in a rectangular tank, which was used to correct any optical distortion. There was an overlow port (D ov = 19.5 mm) located at hal o the tank height, which keeps the liquid level, H luid, at about.35 m. The non-dimensional nozzle diameter, D nozzle /D, or the studies were and the ill height aspect ratio, H luid /D, was 1. The jet nozzles were made rom copper tubing (D pipe = 12.7 mm) with 45 degree elbows with solid stream nozzles (D nozzle = 4.32 mm) attached. The jet nozzles were located.7625 m rom the bottom o the tank. Fluid was supplied to the tank by a.3 hp centriugal pump (McMaster- Carr). A solenoid valve was used to control the pulsing (on/o) action o the jet. To create a pulsing jet, a solenoid valve was used. The valve was able to cycle the luid momentum through the jet nozzle in an on/o manner. One complete cycle, known as the pulse cycle time (t C ), is 5.5s long. The pulse consisted o a discharge time (t D ) o 5 s and an o time o.5 s. this speciic was chosen because it was previously shown to give the best results [15]. Figure 1: Schematic o jet mixer system. Figure 2: Actual jet mixing system used or experimental studies. Mixing time was calculated using a blue dye tracer, which was injected at the bottom o the tank. The concentration o dye was monitored at the outlet as a unction o time using a spectrophotometer (Milton Roy SPECTRONIC 2D). The wavelength o the blue dye was not known beore hand and was measured by plotting the absorbance as a unction o wavelength. Figure 3 displays the absorbance as a unction o wavelengths or a sample. The maximum wavelength (λ max ) ASME 212 Early Career Technical Journal - Vol

5 was ound to be 61 nm. Mixing time was based on a 95% homogeneity criterion, or the time it takes or the concentration in the tank to reach 95 % o the ully mixed concentration. Mathematically, the mixing time can be expressed as m= C C C C <.5 (1) Absorbance Wavelength (nm) Figure 3: Maximum wavelength (λ max ) determined by absorbance vs. wavelength. The dye was also used to monitor mixing behavior and low proiles within the mixing tank. Video and snapshots were captured using a Basler aca24-18 km CMOS camera attached to a PIXC1-E8 rame grabber housed in a computer, all purchased rom Epix, Inc. COMPUTATIONAL METHODS The basic equations which describe the low o an incompressible, Newtonian luid with constant properties are the conservation o mass and conservation o momentum. The conservation o mass and momentum are expressed, respectively, as divv = (2) ρ DV Dt =ρg P+μ V (3) Figure 4 shows the mixing tank model created or simulations to mimic the actual mixing tank used in experiments. ANSYS Fluent was used or all o the CFD simulations. Single and dual jet arrangements are simulated in the current study and the low patterns o each are determined. Figure 5 displays an example o a meshed grid with labeled boundary conditions. Tetrahedral element types were used or meshing. Mesh intervals o 1 2 mm was used. The velocity at the bottom wall was monitored or the dierent mesh intervals. An interval o 15 mm was chosen because it was the largest interval size in which resulted in a grid independent solution. (a) The mixing tank was modeled as a tank with a ree surace where the liquid level was the same as the tank height. The top surace was modeled as a ree shear surace. Outlet conditions were set as an outlow. The no slip condition was set at the tank walls and the jet walls. The inlet velocity rom the jet nozzle was varied to simulate the same jet Reynolds numbers (Re j ) used or experiments. RESULTS Flow patterns created by the jet mixers were visualized using dye tracers and CFD results. Figure 6 displays a schematic o the low patterns created by single and dual jets. As the jet is discharged, part o it is recirculated o the bottom wall and creates a semi-rollover eect. Some o the jet turns into a wall jet and where it travels up the tank to the surace and then a portion o it rolls over and is recirculated through the tank. As the jets are directed downwards, the most prominent low mixing zones are at the top o the tank. Most o the momentum o the jet roll overs due to the side walls and there is not adequate orce to create substantial mixing near the surace. Figure 7 displays the low patterns o dye at captured by snapshots at dierent times or a single jet directed away rom (b) Figure 4: Jet mixer models or (a) single jet and (b) dual jet arrangements. Figure 5: Example o meshed geometry with labeled boundary conditions. ASME 212 Early Career Technical Journal - Vol

6 the tank outlet. The dye was injected slowly, so that the momentum o the dye injection did not greatly aect the results. The most prominent region o low mixing occurs in the area behind the direction o jet discharge. As the luid circulates o the bottom and side walls and travels to the top o the tank, some o the luid exits through the overlow port, which urther inhibits the region behind the jet to become well mixed. Some o the dye motion is due to diusion, rather than solely, convection. (a) (b) (a) (b) Figure 6: Schematic o low pattern created by (a) single jet and (b) dual jets. (c) (d) Figure 7: Snapshots o dye mixing in the jet system at dierent times. Figure 8 shows the pathlines ound rom CFD simulations. The pathlines shows the jet circulating as it hits the bottom and side walls and then travelling to the outlet. Although initially the middle o the tank is not well mixed, ater some time, the middle o the tank starts to get mixed more due to the circulatory patterns created in the tank. The mixing in the center o the tank increases as the low deviates rom being uniorm to more chaotic. The model however does not do a very good job o capturing the eect o the wall jet. This eect can most like be improved by varying the turbulence model and/or the turbulent parameters used in simulations. Figure 9 displays the pathlines or the dual jet mixers. As the jet is injected, it hits the bottom wall and travels towards the surace. Most o the low travels towards the outlet, but some o it recirculates near the middle o the tank. The low mixing zone is located between the two jets at the bottom o the tank. This was noticed during dye studies as well, though the snapshots are not shown. Similar to the single jet, ater a period o time, increased mixing occurs in the middle o the tank as the low becomes more chaotic and the interaction between the circulatory patterns increases. (a) (b) (c) (d) Figure 8: Pathlines o single jet mixer. ASME 212 Early Career Technical Journal - Vol

7 (a) (b) Dimensionless Concentration T M (s) Single Jet Dual Jets Figure 1: Comparison o dimensionless concentration as a unction o time or single and dual jets. (c) MIXING TIME RESULTS The mixing time was measured using experimental methods o turbulent, submerged, jet mixer nozzles. Studies were run or single and dual jet nozzles inclined at 45 rom the horizon, directed towards the bottom o the tank. Studies were run or Re j ranging rom about 6, to 22,. The experimental results are somewhat limited due to the number o sampling locations. Samples o the bulk luid were taken at the tank outlet. This was done as the jets were directed towards the bottom o the tank, where the initial and most rapid mixing would occur. The outlet region is one o the low mixing zones ound or the jet mixers in the conigurations used in the current study, as shown by Figures 7-9, but this may not be the most accurate location. Figure 1 displays an example o dimensionless concentration as a unction o time or a single jet and dual jet. The mixing time was considered as the time in which the dimensionless concentration deviated less than 5% o the inal concentration dierence. The peak height represents the distribution o the dye in the tank to the outlet [3]. The dye was dispersed to the outlet or the dual jets more rapidly than in the single jet coniguration. Figure 11 displays mixing time as a unction o jet Reynolds number or the steady and pulse single jet. As Re j increases, the normal mixing time decreases. This is expected as increasing Re j, can be due to an increase o jet momentum orce into the mixing time, allowing or quicker circulation o luid throughout the tank. (d) Figure 9: Pathlines o dual jet mixers. There is very little dierence between the values o mixing time or the steady jet and the pulse jet, though the pulse jet mixing time is slightly lower. At Re j = 1916, the mixing time o the steady jet was about 9% higher than that o the pulse jet. At Re j = 5625, the mixing time was about 12% higher or the steady jet compared to the pulse jet. Muhammad and Kizito [15] reported that the mixing time was not lower or the pulse jet compared to the steady jet, but a much lower homogeneity criteria was used or mixing time which could account or the or the discrepancy. Mixing Time (s) Re j Steady Jet Pulse Jet Figure 11: Mixing time as a unction o jet Reynolds number single jet coniguration. DUAL JET MIXING TIME Figure 12 shows mixing time as a unction o jet Reynolds number or steady and pulse dual jets. Similarly to the single jet, the mixing time or the steady and pulse jet does not vary ASME 212 Early Career Technical Journal - Vol

8 much. At a combined Re j o about 2, the mixing time o the steady dual jets was about 9% higher than the pulse jets. At a combined Re j o about 7, the steady dual jets had about a 3% higher mixing time than the pulse jet. Mixing Time (s) Mixing Time (s) Re j Continuous Jet Pulse Jet Figure 12: Mixing time as a unction o jet Reynolds number or dual jet conigurations Re j Single Jet Dual Jets Figure 13: Mixing time comparison o single and dual steady jets. Figure 13 compares the mixing time or steady single jet and dual jets. The mixing time is signiicantly reduced with the addition o another jet. At Re j o 163, the mixing time was reduced by about 47% with the addition o another jet. This coincides with results o previous studies, as it was ound that by doubling the number o jets, the mixing time was decreased by hal [15]. Besides adding more momentum in the tank and the additional jet helps eliminates the low mixing zones. Elimination o the low mixing zones is one o the most important actors or enhancing mixing perormance in jet mixed tanks. CONCLUSION The low patterns o single and dual jet mixers were studied using experimental and computational methods. The major low mixing zone or the single jet mixer is located by the jet, opposite o the injection location. The most prominent low mixing zone or the dual jets is between the jets at the bottom o the tank, as the jets are directed outward rom the center. The patterns in the tank are greatly inluenced by the jet location in reerence to the tank walls. The walls and surace help create circulation patterns which enhance mixing and also wall jets, which are not ideal or mixing. The CFD low patterns results were able to model the actual patterns created in the tank using dye airly well. Further improvements can be made to the model to enhance the eect o the wall jet. The mixing time was experimentally studied by injecting a dye tracer. The dye concentration was monitored at the outlet. The mixing time decreased as the jet Reynolds number increased, due to an increase in velocity. The mixing time was decreased or the dual jet mixers compared to the single jet due to an increase in momentum lux and elimination o low mixing zones. Decreasing or eliminating the low mixing zones is possibly the biggest actor inluencing the mixing time. Optimization o the jet mixing tanks (i.e. jet location, height, etc.) can lead to a urther reduction in mixing time and should be explored in urther studies. ACKNOWLEDGMENTS The authors would like to acknowledge the inancial support o the Title III Program at North Carolina A&T State University, which is administered by the U.S. Department o Education, Institutional Development and Undergraduate Education Services. REFERENCES [1] Bathija, P.R., Jet mixing design and applications. Chemical Engineering 1982: p [2] Simon, M. and C. Fonade, Experimental study o mixing perormances using steady and unsteady jets. The Canadian Journal o Chemical Engineering, (4): p [3] Patwardhan, A.W. and S.G. Gaikwad, Mixing in Tanks Agitated by Jets. Chemical Engineering Research and Design, (2): p [4] Rahimi, M. and A. Parvareh, Experimental and CFD investigation on mixing by a jet in a semi-industrial stirred tank. Chemical Engineering Journal, (1-2): p [5] Breisacher, K. and J. Moder, Computational Fluid Dynamics (CFD) Simulations o Jet Mixing in Tanks o Dierent Scales. 21 NASA: Cleveland, OH. [6] Powell, M.R., Onishi, Y., and Shekarriz, R., Research on jet mixing o settled sludges in nuclear waste tanks at Hanord and other DOE sites: A historical perspective. 1997, Paciic Northwest Laboratory: Richland, Washington. p. 9. ASME 212 Early Career Technical Journal - Vol

9 [7] Zughbi, H.D. and I. Ahmad, Mixing in Liquid-Jet-Agitated Tanks: Eects o Jet Asymmetry. Industrial & Engineering Chemistry Research, (4): p [8] Lane, A.G.C. and P. Rice, Comparative assessment o the perormance o the three designs or liquid jet mixing. Industrial & Engineering Chemistry Process Design and Development, (4): p [9] Grenville, R.K. and J.N. Tilton, Turbulent Flow or Flow as a Predictor o Blend Time in Turbulent Jet Mixed Vessels. Proceedings o 9th European Conerence on Mixing, 1997: p [1] Fox, E.A. and V.E. Gex, SINGLE-PHASE BLENDING OF LIQUIDS. AIChE Journal, (4): p [11] Grenville, R.K. and J.N. Tilton, A New Theory Improves the Correlation o Blend Time Data rom Turbulent Jet Mixed Vessels. Chemical Engineering Research & Design, (3): p [12] Fossett, H. and L.E. Prosser, The Application o Free Jets to the Mixing o Fluids in Bulk. Proceedings o the Institution o Mechanical Engineers, : p [13] Maruyama, T., Y. Ban, and T. Mizushina, Jet Mixing o Fluids in Tanks. Journal o Chemical Engineering o Japan, (5): p [14] Tatterson, G.B., Fluid mixing and gas dispersion in agitated tanks. 1991: McGraw-Hill. [15] Muhammad, I.R. and J.P. Kizito, Evaluation o Pulse Jet Mixing Using a Scalar Quantity and Shear Stress. ASME Early Career Technical Journal, : p [16] Tian, X. and P.J.W. Roberts, Mixing in Water Storage Tanks. I: No Buoyancy Eects. Journal o Environmental Engineering, (12): p [17] Furman, L. and Z. Stegowski, CFD models o jet mixing and their validation by tracer experiments. Chemical Engineering and Processing: Process Intensiication, (3): p [18] Zughbi, H.D., Numerical simulation o mixing in a jet agitated horizontal cylindrical tank. International Journal o Computational Fluid Dynamics, 26. 2(2): p [19] Jayanti, S., Hydrodynamics o jet mixing in vessels. Chemical Engineering Science, (1): p [2] Zughbi, H.D. and M.A. Rakib, Investigations o mixing in a luid Jet agitated tank. Chemical Engineering Communications, (8): p [21] Ranade, V.V., Towards better mixing protocols by designing spatially periodic lows: The case o a jet mixer. Chemical Engineering Science, (11): p [22] Parvareh, A., et al., Experimental and CFD study on the eect o jet position on reactant dispersion perormance. International Communications in Heat and Mass Transer, (1): p [23] Zhang, Q. and H. Johari, Eects o acceleration on turbulent jets. Physics o Fluids, (8): p [24] Crow, S.C. and F.H. Champagne, Orderly structure in jet turbulence. Journal o Fluid Mechanics, (3): p [25] Anders, J.W., V. Magi, and J. Abraham, A Computational Investigation o the Interaction o Pulses in Two-Pulse Jets. Numerical Heat Transer: Part A -- Applications, (11): p ASME 212 Early Career Technical Journal - Vol

10 ASME Early Career Technical Journal 212 ASME Early Career Technical Conerence, ASME ECTC November 2 3, Atlanta, Georgia USA COMPARATIVE EFFECTS OF FORCES ACTING ON SWIRLING ANNULAR LIQUID SHEETS Mohammed Ali Department o Technology Jackson State University Jackson, Mississippi, USA Phone: (61) Fax: (61) mohammed.ali@jsums.edu Essam A. Ibrahim Department o Mechanical Engineering The University o Texas o the Permian Basin Odessa, Texas, USA Phone: (432) Fax: (432) Ibrahim_e@utpb.edu ABSTRACT The respective eects o the multiple orces that control the development o swirling liquid sheets injected rom an annular nozzle into quiescent surrounding medium are studied. These orces include inertia, viscous, gravity, pressure, surace tension, centriugal and Coriolis orces. In order to simpliy the mathematical ormulation o the inherently complex transient, three-dimensional problem considered, a body-itted coordinate system is employed. Use o these coordinates enables the transormation o the system partial dierential equations, consisting o mass and momentum conservation equations with appropriate boundary conditions, into ordinary dierential equations. These equations are then solved numerically to yield sheet trajectory, thickness, and velocity, or a given set o mass low rate and liquid-swirler angles. By eliminating any o the acting orces rom the governing equations, one at a time, the individual inluence o each orce on sheet evolution characteristics is isolated and evaluated. It is ound that centriugal and Coriolis orces play signiicant roles in determining the resulting coniguration and low velocities o a developing swirling annular liquid sheet. Whereas centriugal orces act to increase the developing sheet radius and angle, Coriolis orce has opposite eects. The sheet thickness variation is independent o Coriolis orce, but sheet thickness increases signiicantly i the centriugal orce is not taken into account. Neglecting either o the centriugal or Coriolis orces causes the sheet stream-wise velocity to decrease. In the absence o Coriolis orce, the sheet swirl velocity remains constant at its initial value while the centriugal orce has the tendency to diminish swirl velocity. For the range o parameters investigated, gravitational acceleration, surace tension, and interacial riction orces exhibit minimal impact on the ormation o a swirling liquid sheet. The present assessment o the inluence o various orces on the injected sheet behavior may be applied to guide eicient design o swirl injectors. INTRODUCTION To date, most o the transportation, industrial, and power combustion applications o uel atomizers use either pressure, pressure-swirl, or air-blast atomizers [1, 2]. The ormation o thin sheets and the conical nature o the liquid surace emerging rom swirl atomizers ensure more eicient breakup o the liquid into droplets owing to the larger surace energy o the hollow cone. Thereore, or a given liquid supply pressure, the quality o atomization rom a swirl atomizer is superior to that produced by a conventional pressure atomizer. Enhanced atomization leads to a more intimate uel-air mixing, aster evaporation, and hence higher combustion eiciency, which results in reduced uel consumption and pollutant emission. Despite its practical signiicance, the undamental mechanisms o liquid uel sheet injection and atomization are not well understood. In particular, analytical/computational models that accurately predict injection parameters and spray characteristics, such as cone radius and angle, sheet breakup length, drop size, and velocity are lacking. A number o research articles have been published on the theoretical and experimental aspects o an annular sheet emanating rom a nozzle, relevant to dierent practical applications, though mostly not or injectors. Water bells have been considered by Taylor [3] and Baird and Davidson [4]. Research on converging non-swirling annular sheets with reerence to Inertial Coninement Fusion (ICF) reactors has been perormed by Homan et al. [5], Ramos [6, 7], and Hasan et al. [8]. Sivakumar and Rghunandan [9, 1] studied converging swirling annular liquid sheets produced by liquidliquid coaxial swirl atomizers used in bipropellant rockets and elsewhere. The transition o a converging (bell or tulip-shaped) to a diverging (cone-shaped) swirling annular sheet was investigated, both experimentally and theoretically, by Ramamurthi and Tharakan [11, 12]. ASME 212 Early Career Technical Journal - Vol

11 Mao et al. [13], Chuech [14, 15], and Przekwas [16] advanced an analytical/computational model to study the evolution o non-swirling and swirling annular liquid sheets. Their technique is based on the solution o the continuity and momentum equations in a curvilinear co-ordinate system conorming to the sheet boundaries. They reported predictions o the spray angle, ilm thickness and spray velocities that were in general agreement with their experimental measurements. The modeling eort o Chuech [14, 15] was extended by Ibrahim and McKinney [17] who presented a clariied version o Chuech s model that incorporated interacial riction eects. Ibrahim and McKinney s model [17] accounted or most o the various orces that control the progress o a swirling annular liquid sheet emanating rom a nozzle: inertial, viscous, gravitational, surace tension, centriugal and Coriolis orces. The results o this model provided useul inormation on the liquid sheet trajectory, thickness, and low velocity or given nozzle conigurations and mass low rates. The present work is aimed at analyzing the comparative eects each o the multiple acting orces has on the development o a swirling annular liquid sheet issued rom an injector nozzle. The present analysis makes use o the ormulation o Ibrahim and McKinney [17] in perorming the necessary computations. Such an analysis has not been attempted beore, although its results have the potential o improving our understanding o annular liquid sheet ormation. Evaluating the relevant role each o these many orces plays in the evolution o annular liquid sheets is essential to advancing accurate models o uel injection and atomization processes. The evolution o the liquid sheet emanating rom the injector nozzle predetermines its subsequent atomization characteristics, hence uel-air mixing, evaporation, and ultimately, combustion eiciency and stability. Thereore, it is important to improve our understanding o the orces that inluence annular liquid sheet ormation in order to be able to optimize uel injector design or more complete combustion. MODEL FORMULATION As alluded to earlier, Ibrahim and McKinney s [17] model is adopted in the present eort. The basic eatures o the model are summarized here or easy reerence. Ibrahim and McKinney [17] have shown that an annular liquid sheet injected into a quiescent gaseous environment assumes a bell-shape in the absence o swirl but takes the orm o a diverging hollow-cone due to swirl. Only the case o a swirling annular liquid sheet is studied in the present work, owing to its relevance to uel injection applications. A curvilinear coordinate system ξ-ζ-η, as shown in Fig. 1, is utilized as a non-inertial reerence rame to analyze the liquid low in a swirling axi-symmetric hollow-cone sheet emerging rom a nozzle at an initial stream-wise velocity u, tangential velocity w, and cone angle θ in a surrounding gas. The coordinates ξ, ζ, η are perpendicular to each other and coincide with the liquid stream-wise, tangential, and normal to the streamline directions, respectively. The choice o a curvilinear coordinate system that conorms to the sheet boundaries simpliies the mathematical analysis because only the streamwise and tangential velocity components, u and w, respectively, survive while the normal velocity component, v, vanishes. The liquid low is assumed to be Newtonian, incompressible and inviscid, in the sense that viscous stresses are negligible relative to liquid-gas interacial riction. Since in practical spray applications, the sheet thickness is usually much smaller than the cone radius, variations o stream-wise velocity across the sheet thickness may be neglected. Mathematically, the governing equations describing conservation o mass and momentum per unit volume at steady state may be expressed as: Continuity: (1) ( ρ u rδ ) = ξ Momentum in the stream-wise ξ-direction: u sinθ ρ u ρ u w = Sξ + ρ g cosθ ξ r (2) Momentum in the normal η-direction: θ cosθ p ρ u u ρ w w = ρ g sinθ (3) ξ r η Momentum in the tangential ζ-direction: w sin θ ρ u + ρ u w = S (4) ζ ξ r η ξ ζ r θ ds u u u + ds δ ξ δ δ + ds ξ r r + ds ξ z Figure 1. Schematic diagram o an annular liquid sheet where r and z are the cylindrical radial and axial coordinates, respectively, ρ is the liquid density, δ is the local sheet thickness, and θ is the cone/spray angle, deined as the angle between the nozzle axis and the tangent line at the corresponding spray edge location. The irst term in each o Eqs. (2), (3), and (4) represents the directional components o the inertia orces in the stream-wise, normal, and tangential directions. The second term in each o Eqs. (2) and (4) denotes r ASME 212 Early Career Technical Journal - Vol

12 the directional components o the Coriolis orce. The second term in Eq. (3) relates to centriugal orce. The terms ρ g cosθ and ρ g sinθ in Eqs. (2) and (3) designate the directional components o the gravity orce. The terms S ξ and S ζ in Eqs. (2), (3) account or the liquid-gas interacial riction orces in the stream- wise and tangential directions, respectively. The use o primitive variables in the present ormulation is intended to add to the clarity o the model s equations. The pressure gradient in the normal direction η can be approximated by its integrated orm as a unction o the gas pressure dierence across the liquid gas interace and surace tension orces: p p pg 2σ cosθ θ = η δ δ δ r ξ where p is pressure and σ is surace tension. Subscripts and g denote liquid and gas quantities, respectively. The terms inside the bracket represent the axial and meridian radii o curvature, respectively [3]. Following Chuech [14, 15], the viscous orces in the streamwise and tangential momentum equations are accounted or through the interacial riction orces acting on the inner and outer liquid-gas interaces. Thereore, the viscous orces may be written, respectively, in terms o Rizk and Leebvre s [18] gasliquid interacial riction actors representation as: ρg 1/4 Sξ =.79( δ / r)(re ) ξ ( ug u ) ug u 2δ (6) ρg 1/4 Sζ =.79( δ / r)(re ) ζ ( wg w ) wg w 2δ (7) where Re ξ and Re ζ are Reynolds numbers based on the oriice diameter, gas properties, and the absolute value o the dierence between the gas and liquid velocities in the stream wise and tangential directions, respectively. The terms between square brackets in Eqs. (6) and (7) designate Rizk and Leebvre s [18] interacial riction actors. For pressure swirl injectors, the gas velocities in Eqs. (6) and (7) vanish, since there is no gas low involved. Air low in airblast/air-assist injectors maybe assumed to be at a constant velocity through the entire domain, depending on the air pressure drop across the nozzle [13]. Due to the simpliying assumptions and the use o conorming curvilinear coordinates in the present model, all the dependent variables have gradients only in the stream-wise direction, ξ. Thereore, the governing equations (1), (2), (3), (4) subject to Eqs. (5), (6), (7) may be simpliied to a system o nonlinear irst-order ordinary dierential equations in the orm du dr dδ rδ + u δ + u r = (8) dξ dξ dξ u sinθ ρ u ρ u w = Sξ + ρ g cosθ ξ r (9) ρ u u θ ρ w w ξ cosθ p g 2σ cosθ dθ = + ( ) ρ g sinθ r δ δ r dξ (1) w sin θ ρ u + ρ u w = S (11) ζ ξ r Since the system o Eqs. (1), (2), (3), (4) subject to Eqs. (5), (6) and (7) include our equations and ive unknowns, r, θ, δ, u, w, an additional equation is needed to make the system determinate. Such an equation may be derived rom geometrical considerations o the median streamline as shown in Fig. 1. dr =sinθ (12) dξ (5) A set o ive boundary conditions are needed to bring closure to the model. Since the hollow-cone liquid low is bounded at the nozzle oriice, the boundary conditions to be coupled with the system o dierential equations may be stated as r = = R D ξ = θ ξ = θ = δ ξ = δ = u / 2 m = u ξ = = πρ Dδ w = w = u ξ = tanα (13) (14) (15) (16) (17) where subscript denotes initial quantities, R and D are the respective initial sheet radius and diameter, and m is the known uel mass low rate, and α is the uel port/swirler angle. To enable tracking o sheet trajectory, its axial coordinate z is evaluated in reerence with Fig. 1 as dz = cosθ (18) dξ subject to the boundary condition, z = (19) ξ = RESULTS AND DISCUSSION For the present computations the low conditions are taken to be similar to those used by Ibrahim and McKinney [17] to permit direct comparison to their results. Thereore, the annular sheet diameter at the nozzle oriice is D = 6.63 mm. The initial sheet thickness is taken to be, (9) δ =.1524 mm, which is equivalent to 1/4 o the pre-ilmer width and is taken to be invariable with other low conditions. The water sheet is assumed to be injected vertically downward so that initial sheet cone angle, θ =. To study the eects o liquid-port angle, or ASME 212 Early Career Technical Journal - Vol

13 liquid-swirler angle, α, and liquid mass low rate, m, on their calculations, Ibrahim and McKinney [17] varied the port angle between and 6 and considered mass low rates o 17.76, 4.82, and g/s. Since the present study is concerned with examining the contribution o various acting orces to liquid sheet behavior at the same low conditions, a representative port angle o α = 3 and mass low rate o m = g/s are selected or the numerical simulations. The liquid uel properties are density, ρ = 765 kg/m 3, dynamic viscosity, µ = 9.2x1-4 kg/m.s, and surace tension, σ =.25 N/m. The surrounding gas is assumed to be air at atmospheric conditions with density o ρ g = 1.22 kg/m 3 and dynamic viscosity o µ g = 17.9x1-6 kg/m.s. The initial sheet velocities in the stream-wise and tangential directions, u and w, are calculated rom nozzle geometric parameters, liquid properties, and mass low rate. The system o nonlinear irst-order ordinary dierential equations given by (8), (9), (1), (11), (12), and (18), subject to the boundary conditions expressed as (13), (14), (15), (16), (17), and (19) is solved using a ith order Runge-Kutta Verner method to yield solutions or r, θ, z, δ, u, w. In the present model, since the surrounding gas is assumed to be quiescent, quantities representing gas velocity, u g and w g, vanish rom Eqs. (6) and (7), ollowing Chuech and co-authors [13-16] and Ibrahim and McKinney [17]. It is also assumed that the outer and inner gas pressures are equal, so that, p g =. Note that results or a non-swirling annular sheet may be obtained when the liquid swirl velocity, w, is set to zero. The eects o any one o the acting orces on the coniguration and velocities o a developing swirling liquid sheet may be extracted by setting terms corresponding to a particular orce to zero in the governing equations. Thereore, the gravity orce contribution is cancelled by substituting g =, and surace tension is disregarded by using σ =, and interacial riction is eliminated by dropping corresponding terms or S ξ and S ζ rom Eqs. (9) and (11), respectively. The centriugal orce is ignored by deleting the second term in Eq. (1), and the Coriolis orce is not considered i the second term in each o Eqs. (9) and (11) are removed. As will be expounded later, it turns out that neglecting either o gravitational acceleration, surace tension, or gas-liquid interacial riction orces, produces only slight modiication o the swirling annular sheet evolution attributes. Thereore, the eects o centriugal and Coriolis orces are discussed irst. Figures 2 and 3 portray the respective variations o the dimensionless sheet radius and cone angle with dimensionless axial distance measured rom the nozzle exit. Numerical solutions are presented or three cases: (1) all orces in the governing equations are taken into account, (2) centriugal orce is neglected; and (3) Coriolis orce is neglected. It can be seen rom Figs. 2 and 3 that excluding the centriugal orce rom the governing equations would lead to the production o an annular sheet with a radius and angle that slightly increase in the axial direction, but are signiicantly below their corresponding values i the centriugal orce is accounted or. This may be explained by the act that the centriugal orce acts to deorm the sheet in the direction perpendicular to the axis o rotation. Thereore, sheet expansion is substantially hindered by the absence o the centriugal orce. Hence, i a speciic application necessitates a wider hollow-cone sheet, the centriugal orce could be increased to meet that requirement, or example, by increasing the swirler angle α in accordance with Eq. (17). Dimensionless sheet radius, r/d All orces No centriugal No Coriolis Dimensionless axial distance, z/d Figure 2. Eects o neglecting centriugal or Coriolis orce on axial variation o dimensionless sheet Sheet angle, θ All orces No centriugal No Coriolis Dimensionless axial distance, z/d Figure 3. Eects o neglecting centriugal or Coriolis orce on axial variation o sheet angle Figs. 2 and 3 also indicate that, unlike the centriugal orce, excluding Coriolis orce promotes the growth o the sheet radius and angle in the axial direction, with magnitudes that are much greater than when these orces are accounted or. This trend is a consequence o the reduction in the sheet stream-wise velocity that is experienced when the inertial action o the Coriolis orce is disregarded, as will be explicated later. The sheet radius and angle gradually increase in the axial direction, signiying the ormation o a diverging hollow-cone sheet, in accordance with the observations o Ibrahim and McKinney [17]. ASME 212 Early Career Technical Journal - Vol

14 Dimensionless sheet thickness, δ/δ Dimensionless axial distance, z/d Figure 4. Eects o neglecting centriugal or Coriolis orce on axial variation o dimensionless sheet thickness Dimensionless sheet stream-wise velocity, u/u All orces No centriugal No Coriolis All orces.4 No centriugal No Coriolis Dimensionless axial distance, z/d Figure 5. Eects o neglecting centriugal or Coriolis orce on axial variation o dimensionless sheet stream-wise velocity Figure 4 displays the dimensionless sheet thickness variation versus dimensionless axial distance along the nozzle axis. It is noted in Fig. 4 that disregarding the centriugal orce avors a larger annular sheet thickness. This is expected since the sheet radius is smaller than that yielded rom including the centriugal orce in the analysis, as revealed earlier in Fig. 2. Hence, to satisy conservation o mass, the sheet thickness must increase as its radius is reduced. Interestingly, Figure 4 demonstrates that neglecting Coriolis orce doesn t generate much change in the sheet thickness, apart rom that when it is included. With and without Coriolis orce in place, the sheet thickness tends to decrease in the axial direction in a similar ashion. This is may be surprising given that the sheet radius is much larger or the case o negligible Coriolis orce compared to when all modeled orces are represented in the analysis, as the results in Fig. 2 conirm. However, the sharp rise in sheet radius, which occurs in the absence o Coriolis orce, is compensated or by a steep drop in the stream-wise velocity (as will be discussed later), conserving mass in a manner that preserves sheet thickness variation and that mirrors the one dictated by the complete governing equations. The variation o the non-dimensionalized stream-wise velocity variation with the dimensionless axial distance is depicted in Fig. 5. It is evident rom Fig. 5 that, when Coriolis orce is absent, the stream-wise velocity decreases rapidly in the axial direction and is considerably lower than that produced when Coriolis orce is present. This behavior is due to the reduction in sheet inertia associated with subtracting the Coriolis orce. The centriugal orce deduction has a somewhat similar but much smaller eect. Solving the ull governing equations results in a stream-wise velocity that is greater than what is observed i Coriolis or centriugal orces are not included. In this case, the stream-wise velocity exhibits an initial increase, ollowed by a gradual decrease in the axial direction. The initial increase in the stream-wise velocity corresponds to the initial rapid drop in sheet thickness remarked in Fig. 4. As the sheet thickness reduction levels o, the stream-wise velocity starts to decrease because o the increase in sheet radius in the axial direction, as noted in Fig. 2, becomes the dominant actor. Thereore, the behavior o the stream-wise velocity is consistent with mass conservation. Figure 6 illustrates the variation o dimensionless tangential velocity against the dimensionless axial distance in the upstream direction. It is clear rom Fig. 6 that eliminating either centriugal or Coriolis orces leads to an increase in sheet tangential velocity. This observation is the opposite o what has been mentioned or the stream-wise velocity in relation with Fig. 5. It is thereore deduced that inertial eects accompanying centriugal and Coriolis orces act to enhance sheet stream-wise velocity at the expense o tangential velocity. It is worth noting that the sheet tangential velocity remains constant at its initial magnitude i Coriolis orce is nonexistent, as delineated in Fig. 6. Thereore, it is envisaged that modulations o sheet Dimensionless sheet tangential velocity, w/w All orces No centriugal No Coriolis Dimensionless axial distance, z/d Figure 6. Eects o neglecting centriugal or Coriolis orce on axial variation o dimensionless sheet tangential velocity ASME 212 Early Career Technical Journal - Vol

15 tangential velocity are imparted solely by Coriolis orce. As noticed in Fig. 6, solutions o the ull governing equations disclose a monotonic decrease in sheet tangential velocity in the axial direction. The reduction in tangential velocity is related to the increase in sheet radius and angle reported in Figs. 2 and 3. Table 1. Numerical simulation results considering all modeled orces z/d r/d θ δ/δ u /u w /w Tables 1-4 document numerical solutions o the governing equations or our cases: (1) all modeled orces are considered; (2) gravity orce is neglected; (3) surace tension orce is neglected; and (4) interacial viscous orces are neglected, respectively. As can be seen in Tables 1-4, only minute dierences exist between the solutions or these our scenarios. So, these results are mainly presented here or completeness. However, some minor dierences in some o these results warrant comment. For example, comparison o the results in Tables 1 and 3 point to a slightly larger sheet radius and cone angle, or curvature, paralleled by a little reduction in sheet thickness and velocities, to conserve mass, in the absence o the contracting action o surace tension orce. In addition, contrasting the results o Tables 1 and 4 exposes that, to a small extent, sheet velocities are increased while sheet thickness, radius, and angle are moderated, due to the lack o the dissipating, i.e. decelerating, eects o interacial riction orce. Hence, it is concluded that, or the range o parameters scrutinized, the orces o gravity, surace tension, and interacial riction wield only minimal deviations in sheet evolution characteristics. Table 2. Numerical simulation results neglecting gravity orce z/d r/d θ δ/δ u /u w /w CONCLUSIONS The present work sheds a light on the contribution each o the various orces acting on a swirling annular liquid sheet makes to its evolution characteristics. The use o a body-itted Table 3. Numerical simulation results neglecting surace tension orce z/d r/d θ δ/δ u /u w /w ASME 212 Early Career Technical Journal - Vol

16 z/d r/d θ δ/δ u /u w /w Table 4. Numerical simulation results neglecting interacial riction z/d r/d θ δ/δ u /u w /w non-inertial reerence rame, in which centriugal and Coriolis orces maniest themselves, enabled a deeper insight about their important role in determining the outcome o the developing swirling annular sheet proile and directional velocities. Thus, these orces could be manipulated to induce desired outcomes. The present results indicate that Coriolis orce promotes sheet stream-wise velocity while simultaneously diminishing sheet radius, angle, and tangential velocity. The centriugal orce acts to reduce sheet thickness and velocities while supporting a more pronounced sheet radius and angle. Whereas it might be obvious to most researchers that the centriugal orce is essential to modeling the behavior o injected annular swirling liquid sheets, the present study proves beyond doubt that Coriolis orce is also indispensable to ensuring a model s physical integrity. For the range o liquid properties and low conditions investigated, gravity, surace tension, and gas-liquid interacial viscous orces exhibit undetectable inluence on the swirling annular sheet developmental eatures. The plausibility o the predictions o the model employed in the present numerical simulations casts conidence on the model s accuracy. Since in uel injection applications the sheet eventually disintegrates into drops, model predictions o sheet trajectory, thickness, and velocities resolve resultant ligament and drop sizes, orientation and velocities. Thereore, this model may be linked to a sheet breakup model to seamlessly tie the injector geometrical and operating conditions to the inal upshot o liquid atomization processes. Thus, the inluence o an injector s design parameters on its unctionality can be extracted and exploited in enhancing uel injector design and hence combustion perormance. REFERENCES [1] Leebvre, A., H., 1989, Gas Turbine Combustion, Hemisphere Publishing, New York. [2] Bayvel, L., and Orzechowski, Z., 1993, Liquid Atomization, Taylor and Francis, New York. [3] Taylor, G. I., 1959, The Dynamics o Thin Sheets o Fluid: I. Water Bells, Proceedings o the Royal Society o London, Series A: Mathematical and Physical Sciences, 253(1274), pp [4] Baird, M. H. I., and Davidson, J. F., 1962, Annular Jets-I, Chemical Engineering Science, 17(1), pp [5] Homan, M. A., Takahashi, R. K., and Monson, R. D., 198, Annular Liquid Jet Experiments, ASME Journal o Fluids Engineering, 12(9), pp [6] Ramos, J. I., Liquid Curtains: I. Fluid Mechanics, 1988, Chemical Engineering Science, 43(12), pp [7] Ramos, J. I., 199, Analytical, Asymptotic and Numerical Studies o Liquid Curtains and Comparison with Experimental Data, Applied Mathematical Modeling, 14(4), pp [8] Hasan, M. Z., Mitsutake, Y., Monde, M., 1997, Shape o an Annular Liquid Jet, ASME J. Fluids Engineering, 119(9), pp [9] Sivakumar, D., and Raghunadan, B. N., 1997, A Study on Converging Thin Annular Jets, ASME Journal o Fluids Engineering, 119(12), pp [1] Sivakumar, D., and Raghunadan, B. N., 22, Converging Swirling Liquid Jets rom Pressure Swirl Atomizers: Eect o Inner Air Pressure, Physics o Fluids, 14(12), pp [11] Ramamurth, K., and Tharakan, T. J., 1995, Experimental Study o Liquid Sheets Formed in Coaxial Swirl Injectors, AIAA J. Propulsion and Power, 11(6), pp [12] Ramamurthi, K., and Tharakan, T. J., 1998, Flow Transition in Swirled Liquid Sheets, AIAA Journal, 36(3), pp [13] Mao, C. P., Chuech, S. G., and Przekwas, A. J., 1991, An Analysis o Pressure Swirl and Pure Airblast, Atomization, Atomization and Sprays, 1(2), pp [14] Chuech, S. G., 1992, Numerical Simulation o Nonswirling and Swirling Annular Liquid Jets, 3 th Aerospace ASME 212 Early Career Technical Journal - Vol

17 Sciences Meeting, Reno, NV, 6-9 January 1992, AIAA Paper [15] Chuech, S. G., 1993, Numerical Simulation o Nonswirling and Swirling Annular Liquid Jets, AIAA Journal, 31(6), pp [16] Przekwas, A. J., 1996, Theoretical Modeling o Liquid Jet and Sheet Breakup Process, Recent Advances in Spray Combustion: Spray Atomization and Drop Burning Phenomena, AIAA Inc., 1, pp [17] Ibrahim, E. A., and McKinney, T. R., 26, Injection Characteristics o non-swirling and Swirling Annular Liquid Sheets, IMechE Journal o Mechanical Engineering Science, 22(2), pp [18] Rizk, N. K., and Leebvre, A. H., 198, The Inluence o Liquid Film Thickness on Air Blast Atomization, ASME Journal o Engineering or Power, 12 (7), pp ASME 212 Early Career Technical Journal - Vol

18 ASME Early Career Technical Journal 212 ASME Early Career Technical Conerence, ASME ECTC November 2 3, Atlanta, Georgia USA CLOUD HEIGHT MEASUREMENTS IN JET MIXED TANKS Ibraheem R. Muhammad and John P. Kizito Department o Mechanical Engineering North Carolina A&T State University Greensboro, NC, USA ABSTRACT Jet mixers can be used as an alternative to conventional mechanical mixers or solid suspension processes. In the present study experiments were run to evaluate the suspension o solid particles in a jet mixed tank. The cloud height, or the distinct interace at which no solids are suspended beyond, is measured using three dierent silica dioxide particles. The eect o jet nozzle clearance rom the bottom o the tank and the eect o jet Reynolds number (Re j ) is studied or the dierent particles. Results show that the cloud height increases as the Re j is increased. As particle size increased, the dimensionless cloud height decreased as the drag orce is dominated by the weight o the particle. As the jet nozzle clearance was lowered, the cloud height decreased slightly. For an average particle size o 12 µm with the jet positioned.7625 m rom the bottom o the tank, about 9% homogeneity was achieved. A physical model was developed to predict the cloud height based on a orce balance o a single, spherical particle. The model was able to predict the particle rise airly well at Re j greater than 25. Several recommendations or improvements in the model and uture studies were made. NOMENCLATURE A p Area o spherical particles (m 2 ) Ar Archimedes number C D Drag coeicient C j Constant used or geometrical conditions d p Particle diameter (m) D Tank diameter (m) D j Jet nozzle diameter (m) D ov Overlow port diameter (m) Drag correction coeicient F AM Added mass orce (N) F D Drag orce (N) F B Buoyancy orce (N) F G Gravity orce (N) g Gravity acceleration constant (m/s 2 ) H Tank height (m) H c Cloud height (m) * H c Dimensionless cloud height (H * c = H c /H) Liquid level height (m) H luid H j Jet nozzle clearance (m) m p Mass o spherical particle (kg) Re j Jet Reynolds number (Re j = V D nozzle /υ) U Velocity o bulk luid (m/s) U p Particle velocity (m/s) V Jet velocity (m/s) V t Terminal velocity (m/s) w s Solids weight percent z Distance to any location along the path o the jet (m) Greek symbols µ Dynamic viscosity (N s/m 2 ) υ Kinematic viscosity (m 2 /s) ρ L Liquid density (kg/m 3 ) ρ p Particle density (kg/m 3 ) Φ s Solids volume raction INTRODUCTION The suspension o solid particles is an important process in many applications, including chemical reactions, biological processing, and environmental remediation (i.e. sludge removal). The most common mixers are mechanical agitators, such as impeller mixed stirred tanks. However, jet mixers can be used as an alternative and have even been reported to be just as eicient as impeller mixed systems while using less energy [1]. They operate by withdrawing luid rom the mixing tank and discharging it back into the tank through a nozzle at high velocities. They are especially appealing as they operate with no moving parts, they are easily installed, and they provide high turbulence and shear rates, which are advantageous or mixing processes. Since the jet mixers operate without moving parts, they are especially useul or processes in which maintenance o the mixing equipment can be hazardous Jet mixers have been studied or decades now [2-8], but there is not a lot o literature on the use o jet mixers or solid suspension processes. Bathija [1] studied jet mixing applications and reported a design process or jet mixers in solid suspension processes. Shamlou and Zolagharian [9] determined the just suspension velocity o the jets as a unction o jet nozzle diameter, height, solid particle size, and particle density. Kale and Patwardhan [1] studied the eect o nozzle diameter, nozzle clearance, particle size, nozzle angle, and solids loading on the power necessary or solid suspension. They also provided a semi-empirical model or prediction. ASME 212 Early Career Technical Journal - Vol

19 The perormance o solid suspension processes is usually measured by cloud height, particle dispersion, or cleared area o the bottom o the tank, or amount o solids suspended. The current study ocuses on cloud height. The cloud height can be deined as the level at which most o the particles gets suspended. Some authors deine this as the point at which no urther particles are suspended upon. It can also be viewed as the height at which there is a sharp change in the solids concentration [11]. This is more likely to occur in systems with a high concentration o solids. The purpose o the current study is to determine cloud height in jet mixed tanks. The jet Reynolds number is varied along with particle size. The height o the jet nozzle rom the bottom o the tank is also varied. The results can be used to urther enhance solid suspension processes using jet mixers. A physical model is developed based on the particle motion o a single particle. SOLID SUSPENSION MECHANISM IN JET MIXERS Solid suspension in jet mixers occurs dierently than in mechanical mixers. As the jet is discharged, a ree jet orms, which expands until it impinges on the solids bed, or tank bottom. A wall jet is ormed and results in solid particles rolling over outwardly rom the impingement location. I the velocity is high enough, this creates a region on the bottom o the tank which is ree o solids, known as the eective cleaning radius [12]. This also creates a mound o particles along the outer edge o the tank. At a higher velocity, instead o just rolling, solids begin to start suspending in the bulk luid. Once a particle gets suspended, the low ield o the liquid jet and its interaction with the particle determines how the particle behaves. The low ields o liquid jets are known so prediction o particle behavior once suspended can be predicted. I the upward velocity o the luid throughout the tank is not suicient, the terminal velocity o the particle will cause the particle to all. The particle will either all back to the bottom o the tank or to a point in which the drag overcomes the weight o the particle. EQUATIONS For o-bottom suspension to occur, the hydrodynamic orce o the jet must overcome the weight o the particles. Once suspended, weight, drag, and buoyancy orces all become very important. The terminal velocity o a particle is determined rom a orce balance and is written as = 4 3 (1) The drag coeicient can be easily measured rom experiments. In the Stokes regime, the terminal velocity can be expressed as = 18 (2) An important dimensionless parameter is the Archimedes number, Ar, which is expressed as [13] = (3) The Ar increases as the particle diameter increases. For large Ar (Ar >1), the weight o the particle tends to become more dominant than the drag orce and homogeneity in the system is not created [13]. Other important dimensionless quantities include the particle Reynolds number and the Froude number, shown below respectively. = (4) = (5) NUMERICAL MODEL A physical model was developed to estimate the height rise o particles. The model was based on the suspension mechanism previously described in which the motion and suspension o particles is due to the wall jet that is created once the jet impinges on the particle bed. The model assumes that the particles are spherical and particle-particle interaction is not considered. For initial development o the model, a single particle is used. It is also assumed that the particle reaches equilibrium when the settling velocity o the particle is balanced by the upward velocity o the jet. Rajaratnam [14] ound that a three-dimensional, Newtonian, turbulent jet velocity can be expressed as = The jet velocity at point z, u(z), does not depend on whether the jet is impinging on walls or boundaries or just a wall jet. The constant, C j, is a parameter which accounts or geometry and is usually between 5-6 or turbulent, circular jets. For the current study, equation (6) will be used to represent the velocity at any point along the primary travelled path o the jet. This velocity will represent the velocity o jet that is responsible or suspending the particles. The initial particle velocity was assumed to be equal to the jet velocity at the bottom corner o the tank base or solids bed. So the initial location, z o, was set to H j + D/2. A orce balance was completed on a single particle to orm an expression to measure the motion o a single, spherical particle. The steady orces acting on a single particle include drag, weight, and buoyancy. Also, a term or added mass is added to account or the inertia added due to a particle (6) ASME 212 Early Career Technical Journal - Vol

20 accelerating through the bulk luid and displacing the bulk luid as it travels. The drag orce is expressed as = 1 2 (7) where the drag coeicient, C D, depends on Re p. For intermediate low outside o the Stokesian regime, C D can be expressed as = 24 (8) where is a drag correction coeicient. The Re p in the model was slightly dierent than the one presented previously in equation (4). The Re p in the model is based on the slip velocity as = The correction coeicient used or the model is based on the widely used Schiller Naumann drag coeicient [15] which is written as (9) = (1) The buoyancy and gravity orce is expressed, respectively, as The added mass term is written as = 1 6 (11) = 1 6 (12) = 1 12 (13) The added mass is an important term as it gives an inertial mass which is dierent than the gravity mass. This values are much dierent when the density o a particle is close to that o the luid [16]. For the study at hand, the density o the particles and luid are o the same magnitude. By combining all o the orces, the balance on a single particle becomes = (14) The resulting equation or particle motion is based on the instantaneous velocity o the bulk luid. The velocity o the particle is solved or and subsequently, the height o the particle is obtained rom = (15) where x is the position o the particle. All numerical methods were completed using MATLAB. Equation (14) is discretized using an Euler iterative process. To account or the non-linearity o the irst term on the right hand side o equation (14), one o the slip velocities was solved at the present time step (i.e. t + dt), while the other slip velocity was set to the previous time step (i.e. t). the iteration process continued until the convergence criterion was met. the distinct interace between luids and particles is ormed due to the balancing o the downward velocity o the particles and the upward velocity o the luid at the wall, which is a result o the jet [17]. So or the current study, iterations were run until the upward velocity equaled the terminal velocity o the particles. EXPERIMENTAL METHODS A schematic o the experimental tank is shown in Figure 1. All experiments were run in a.35 m (12 ) clear, polycarbonate, and cylindrical tank. The tank was equipped with an overlow port (D ov = 19.5 mm) such that the liquid height, H luid, remained at.35 m. The diameter o the jet nozzles used or experiments was 4.32 mm. The nozzle was centered in the tank and directed downward at a clearance height (H j ) o.7625 and.38 m rom the bottom o the tank. The orientation o jets were used in previous jet mixing studies [5]. The jet orientation is such that the jets are able to create a circulatory pattern due to jet impinging on the tank walls. Only one nozzle was used in the present study. A.3 hp centriugal pump was used to supply the luids to the mixing tank. Water was used as the working luid. The velocity o the jet was varied rom about m/s. The jet Reynolds number (Re j ) varied rom about Various silicon dioxide particles (U.S. Silica) were used or experiments. For each sample, the size distribution o the particles varied. The d5 particle size, or the diameter at which 5% o the solids are iner, was used. Figure 2 shows the size distribution or the solids used. Table 1 summarizes the properties o the particles. A solids volume raction, Φ s, o.45 and weight percent o solids, w s, o 1.6% was used or all tests. ASME 212 Early Career Technical Journal - Vol

21 .1525 m.7625 m (a) (b) Figure 1: Schematic o mixing tank used in experiments. Figure 3 shows microscopic images o the dierent particles used in experiments. The images show that particles are not spherical. The d5_12 and d5_265 particles are classiied as subangular and the d5_7 particles are angular. % Passing thru Sieve Microsil CGS Mapleton #1 Glass Mystic White II Particle Diameter (µm) Figure 2: Size distribution or solid particles The cloud height was measured as Re j was varied. The steady jet was initiated and as the solids suspended, a distinct interace was observed. The entire process was recorded using a Basler aca24-18 km CMOS camera attached to a PIXC1- E8 rame grabber housed in a computer, all purchased rom Epix, Inc. A solid state green laser (MGH-H-532, Opto Engine, UT, USA) was used to illuminate regions o the tank. The cloud height was considered the maximum ormed interace ater a period o time. The interace was not always constant and so a high and low value was recorded or each run. (c) Figure 3: Microscopic images or (a) Microsil CGS (d5_12), (b) Mapleton #1 Glass (d5_265), and (c) Mystic White II (d5_7) particles Table 1: Properties o solid particles Microsil CGS Mapleton #1 Glass Mystic White II Sample No. d5_12 d5_265 d5_7 Mineral Quartz Quartz Quartz d5 (µm) Speciic Gravity Grain Shape Subangular Subangular Angular ph V t (m/s) Ar * Re p RESULTS The observed cloud height was measured using nonintrusive optical techniques. Figure 4 shows a snapshot o the observed cloud height. It can be seen where the distinct interace is shown and how the high and low cloud height values were calculated. Some additional particles were noticed above the line, but there were not included in determining the cloud height. Those outlier particles were due to the range o particle sizes in each run. An actual scale was placed in the image to accurately measure the height. Though, not the ocus o the current study, the gray scale intensity decreases as with increased height, due to the gradients in particle size. By ASME 212 Early Career Technical Journal - Vol

22 calibration o the gray scale intensity, an estimate o axial concentration can be determined through analysis. H c * H c,low Figure 4: Snapshot o cloud height H c,high Re j d5_12 d5_265 d5_7 Figure 5: Maximum dimensionless cloud height at a jet nozzle height o.7625 m The maximum cloud height was determined with the jet nozzle positioned at.7625 m and.38 m rom the bottom o the tank. The cloud height was non-dimensionalized using the liquid ill level height. Figure 5 displays the maximum cloud height measured or the three dierent particle samples at a nozzle height o.7625 m as a unction o Re j. Overall, there was an increase in cloud height with increase in jet velocity and ultimately Re j. Once a jet Reynolds number o about 238 was reached, there was a steeper increase in cloud height. Since the d5_12 particles had the smallest diameter and the lowest terminal velocity, they were easily suspended. About 9% homogeneity was achieved using the d5_12 particles at Re j = 285. At the same Re j, only 19% homogeneity was achieved using the d5_7 particles. This can be due to the larger particles colliding with one another and decreasing the kinetic energy o the particles [18]. More suspension can be achieved by providing more kinetic energy rom the jet. Much suspension was not expected or the large particles as the Ar is so high, meaning the gravity orce is more dominate than the drag orce. Figure 6 shows the minimum dimensionless cloud height or the three particle sets at a nozzle height o.7625 m. At a Re j o about 83, the jet orce was not suicient to create a uniorm radial cloud height or the d5_265 and d5_7 particles. The minimum cloud height was measured as when the cloud height did not extend out to the complete diameter o the tank. H c * Re j d5_12 d5_265 d5_7 Figure 6: Minimum dimensionless cloud height at a jet nozzle height o.7625 m Figure 7 displays the dimensionless cloud height as a unction o Re j or a jet nozzle positioned.38 m rom the bottom o the tank. The maximum and minimum values o cloud height are displayed. The minimum results or the d5_7 particles are not shown because they were all equal to, as the cloud did not extend the ull diameter o the tank. As the nozzle was closer to the solids bed, the maximum homogeneity did not exceed 25%. For the largest particles, d5_7, a jet Reynolds number o 83 was not able to suspend the particles. With the jet positioned lower, the homogeneity in the tank was lowered. The jet was absorbed by the particles and there was not enough orce to suspend the particles. When the ree jet impinged on the solids, it turned into a wall jet. Even or the largest particles, when no suspension occurred, particles were dispersed outward rom the center and created mounds around the edges o the tank. I the velocity o the jet is increased, the particles would then be suspended [1]. As the jet is discharged, it expands radially, but when the jet is closer to the bottom o the tank, its expansion is limited. Although a wall jet is then created, i the velocity o the wall jet is not suicient, suspension will not occur. The lowered expansion also was a actor in the cloud height not being able to expand the complete diameter o the tank. Figure 8 shows a comparison o the dimensionless cloud height or both jet heights as a unction o Fr. At Fr = 514, at both heights, more than 6% homogeneity was achieved. At Fr ASME 212 Early Career Technical Journal - Vol

23 = 44, the dimensionless cloud height did not exceed 1% o the total liquid height. The minimum cloud height value does not vary much at the two dierent heights. At higher Fr, the lower nozzle clearance provided cloud heights greater than that at the higher clearance level. H c * H c * Re j Max, d5_265 Min., d5_265 Max, d5_7 Min., d5_7 Figure 7: Dimensionless cloud height or jet nozzle at a height o.38 m Max., Hjet =.7625 m Min., Hjet =.7625 m The results o the physical model and experimental results were compared to determine the validity o the model. Figure 9 shows the comparison between the experimental and physical model results or the dp5_265 particles. At Re j greater than 25, the model predicts the cloud height well. At the two highest Re j, the maximum deviation rom the experimental values was only 4.6%. However, there is larger error rom the experimental results at a Re j o 238 and 83. Figure 1 shows a comparison o experimental and model results or the d5_7 particles. The model predicts the cloud Fr Max., Hjet =.38 m Min., Hjet =.38 m Figure 8: Comparison o dimensionless cloud height as a unction o Fr or d5_265 particle sample height very accurately at Re j o 28 and 285. The maximum error rom the experimental results is only 2%. The error increases as the Re j decreases. This is similar to the results o the d5_265 particles. This could be due to the drag model which was used. The model or drag coeicient is a unction o Re p, but it is most accurate at intermediate Re p values. The model could be improved by incorporating dierent drag coeicient models or the various Re p ranges. H c * H c * Re j Experimental Model Figure 9: Comparison o experimental and physical model results or the d5_265 particles Re j Experimental Model Figure 1: Comparison o experimental and physical model results or the d5_7 particles The results o the physical model or the d5_12 particles are shown in Figure 11. The model predicts that the tank would be ully mixed at Re j greater than 238. Further improvements in the model should be made, but some o the error can be attributed to the drag model used. However, at a Re j o 83, the model predicts the non-dimensional cloud height very accurately. There was only.2% error rom the experimental results at a Re j o 83. ASME 212 Early Career Technical Journal - Vol

24 During experiments at low Rej (i.e. 83), the cloud did not extend the ull diameter o the tank or the d5_265 and d5_7 particles. To account or this in the model, multiple particles should be used. For example, a statistical approach should be used to account or the varying particle height. However, the model does predict the height o a single particle correctly. The model predicted that at a Re j o 83, the particle rose very slightly with a diameter o 265 and 7 µm. Since, experiments showed that the cloud height did not extend the ull diameter o the tank, the model is actually accurate. For the d5_12 particles, the model predicted that the particle orces were not able to equilibrate within the height o the tank and thus it rose to the liquid height o the tank. When measuring the cloud height, there may be outlier particles which extend above the measured cloud height. So the model does predict the single particle well. H c * Re j Experimental Model Figure 11: Comparison o experimental and physical model results or the d5_12 particles The model presented in the present study is just an initial model and urther improvements should be made to increase its accuracy in predicting cloud height. For instance, the model is based on a single particle, whereas in the actual experiments, a solids weight percent o 1% was used. At such solids loading, other phenomena like particle-particle interaction should be accounted or. Another assumption used in the current model was the particles were spherical. The actual particles used in experiments are clearly not spherical as shown in Figure 3. It is expected that spherical particles and non-spherical particles behave dierently. Further studies should include model parameters to account or geometrical dierences in the particles. Also, the model should be tested using spherical particles. Though equation (6) given by Rajaratnam has been tested and well documented, a more accurate model or the wall jet created by impinging liquid jets should be used. Another suggestion is to improve the drag unction used. Not only should the drag be a unction o the dierent ranges o Re p, but it should account or the change in drag as an eect o proximity to boundaries and additional particles. CONCLUSION Studies were run studying the eect o Re j on the cloud height achieved in jet mixed tanks. The jets were placed at two dierent heights,.7625 and.38 m, rom the bottom o the tank. The percent o homogeneity was increased as the Re j increased. The level o solids suspension was lowered when the jet was placed closer to the solids bed. The jets did a good job o suspending particles with a d5 size distribution o 12 µm as 8% homogeneity was achieved. The model that was developed was able to predict the cloud height well or Re j greater than 238 or the particles with a mean diameter o 265 and 7 µm. The error in these systems increased as Re j decreased. For the smallest particles, the model was able to accurately predict the cloud height at Re j o 83, but there was error or the larger Re j. The model actually predicted the entire tank to be homogenized above Re j o 83. Several recommendations or improvements in the model were made including modiying the drag coeicient or a wider range o Re p and including eects o walls and particles on the drag. Also recommendations or the wall jet that is responsible or particle suspension should be improved. Since the model was developed or a single, spherical particle, modiications should be made to account or dierences in particles and the particle-particle interaction phenomenon. The results rom the present study can be used to help optimize jet mixing systems. By knowing, the cloud height in a mixing tank, correct locations can be chosen when pumping the solids out o the mixing tank to another tank. This can be especially useul in the suspension o sludge in storage tanks, where the suspended solids needs to be pumped out or urther processing. Suspension o solids using jet mixers can possibly be improved, but urther studies need to be run or optimization. For example, uture studies should include multiple jets, eect o jet angle, and higher Re j. Other studies can be run where axial concentration proiles are determined. ACKNOWLEDGMENTS The authors would like to acknowledge the inancial support o the Title III Program at North Carolina A&T State University, which is administered by the U.S. Department o Education, Institutional Development and Undergraduate Education Services. REFERENCES [1] Bathija, P.R., Jet mixing design and applications. Chemical Engineering 1982: p [2] Fossett, H. and L.E. Prosser, The Application o Free Jets to the Mixing o Fluids in Bulk. Proceedings o the Institution o Mechanical Engineers, : p [3] Grenville, R.K. and J.N. Tilton, Turbulent Flow or Flow as a Predictor o Blend Time in Turbulent Jet Mixed Vessels. Proceedings o 9th European Conerence on Mixing, 1997: p ASME 212 Early Career Technical Journal - Vol

25 [4] Lane, A.G.C. and P. Rice, Comparative assessment o the perormance o the three designs or liquid jet mixing. Industrial & Engineering Chemistry Process Design and Development, (4): p [5] Muhammad, I.R. and J.P. Kizito, Evaluation o Pulse Jet Mixing Using a Scalar Quantity and Shear Stress. ASME Early Career Technical Journal, : p [6] Zughbi, H.D., S.W. Siddiqui, and A.I. Fatehi, Mixing in a Fluid Jet Agitated Tank: Geometric Eects. Developments in Chemical Engineering and Mineral Processing, (1-2): p [7] Patwardhan, A.W. and A.R. Thatte, Process Design Aspects o Jet Mixers. The Canadian Journal o Chemical Engineering, (1): p [8] Furman, L. and Z. Stegowski, CFD models o jet mixing and their validation by tracer experiments. Chemical Engineering and Processing: Process Intensiication, (3): p [9] Shamlou, A. and A. Zolagharian, eds. Suspension o Solids in Liquid Jet Stirred Vessels. Fluid Mixing 4, ed. H. Benkerian. 199, Instn. Chem. Eng. Symp. Series: New York, NY [1] Kale, R.N. and A.W. Patwardhan, Solid Suspension in Jet Mixers. The Canadian Journal o Chemical Engineering, (5): p [11] Wu, J., et al., High solids concentration agitation or minerals process intensiication. AIChE Journal, (9): p [12] Hamm, B.A., W.L. West, and G.B. Tatterson, Sludge suspension in waste storage tanks. AIChE Journal, (8): p [13] Mersmann, A., et al., Theoretical prediction o the minimum stirrer speed in mechanically agitated suspensions. Chemical Engineering and Processing, (6): p [14] Rajaratnam, N., ed. Turbulents jets. Developments in Water Science, ed. V.T. Chow. 1976, Elsevier Scientiic Publishing Company: Amsterdam. [15] Schiller, L. and A. Naumann, Uber die grudlegenden Berechungen bei der Schwerkratarbereitung. Ver. Deut. Ing., : p [16] Mordant, N. and J.F. Pinton, Velocity measurement o a settling sphere. The European Physical Journal B - Condensed Matter and Complex Systems, 2. 18(2): p [17] Bittor, K.J. and S.M. Kresta, Prediction o Cloud Height or Solid Suspensions in Stirred Tanks. Chemical Engineering Research and Design, (5): p [18] Ochieng, A. and A.E. Lewis, CFD simulation o solids obottom suspension and cloud height. Hydrometallurgy, (1-2): p ASME 212 Early Career Technical Journal - Vol

26 ASME Early Career Technical Journal 212 ASME Early Career Technical Conerence, ASME ECTC November 2 3, Atlanta, Georgia USA THE EFFECT OF VARIOUS GURNEY FLAP SHAPES ON THE PERFORMANCE OF WIND TURBINE AIRFOILS Mohammad Mohammadi, Ali Doosttalab Undergraduate, K.N.Toosi Univ. o Technology Tehran, Iran Mehdi Doosttalab R&D Engineer, Nordex Energy GmbH Hamburg, Germany ABSTRACT This paper gives an overview on two-dimensional numerical investigation and comparison o aerodynamic characteristics o small laps used to increase lit on wind turbine airoils. The small laps consist o Gurney laps, trailing edge wedges and a devised trailing edge curved shape. The investigations were perormed or a diversity o lengths and heights o these laps on the TU Delt DU 91-W2-25 airoil. Extensive numerical simulations has been done using RANS model using SST-Transitional turbulence model using a commercial CFD code, a CFD inite-volume based sotware, at the Reynolds number o The results conirmed advantages o using the trailing edge curved shape over the Gurney lap, which will be more eicient as the lap height is increased. INTRODUCTION The Gurney lap is a small lap utilized to increase the lit coeicient o an airoil. The application o increased lit coeicient is that or a given airoil the chord, C, could be reduced to a comparable amount so that the generated lit still equals that o the original airoil [1]. During the last decade due to the increase o the oil price, the size o the new generation wind turbines with a higher power production capacity increased rapidly, and designing such kinds o the wind turbines becomes a real challenge or designers, because they should be lightweight, and have low production costs, while maintaining aerodynamic perormance. The beneits o this reduced chord length are that the weight and the material expenses or building the blades will be reduced. The gurney lap was developed and applied to race cars by Robert Liebeck and Dan Gurney in 196 s [2]. The concept involves o a small tab located at the trailing edge o an airoil. The tab was deployed to a height on the order o the boundary layer thickness (1-2% o chord length) [3, 5]. It was observed that increasing lap size over 2% o chord length noticeably increased the drag even though there was continuing increase in lit. The aerodynamic orce alteration is consequence o a small region o separated low directly upstream o the lap with two counter-rotating vortices downstream o the lap eectively modiying the trailing edge Kutta condition [4]. Although using Gurney lap increases the lit coeicient, in return, it also reduces lit-to-drag (L/D) ratio which will increase drag orce that the wind turbine base has to withstand. There is also a device called trailing edge wedge that is a wedge located at the trailing edge o the airoil [3]. It also increases the lit coeicient not as much as the Gurney lap but the L/D ratio is better than o a Gurney lap. In this study the characteristics o a new optimized curved shape located at the trailing edge were investigated, giving a divergent trailing edge as a control device, the ocus o current study is to compare lit coeicient and L/D ratio o this new device to Gurney lap and Trailing edge wedge. In this paper the steady-state numerical computations using transitional RANS model or a diversity o trailing edge wedges and corresponding trailing edge curved shape as well as angle o attacks at the Reynolds number o on the DU 91- W2-25 [6,7] airoil were studied. The shape o the airoil is depicted in Figure 1. Traditional RANS turbulence models Y/C X/C Figure 1. The DU 91-W2-25 airoil usually assume that the low is entirely in a turbulent state. However, the laminar to turbulent transition may occur on the ASME 212 Early Career Technical Journal - Vol

27 surace o the airoil. That is to say, considering the transition can enhance the accuracy o numerical simulations under certain circumstances. NUMERICAL METHODS AND GRID To simulate the low ield, a commercial inite volume CFD code was used as a low solver. The two-dimensional incompressible RANS (Reynolds-Averaged Navier-Stokes).1.5 Y/C H X/C Figure 3. DU 91-W2-25 airoil with 1% o cord length Gurney lap Figure 2. Grid distribution around the airoil turbulence model, which was used in this investigation, is the our equations SST-Transitional RANS model to simulate the transition o the low over airoil. The discretization scheme or all equations was the second-order upwind scheme. Moreover, a commercial grid generator was used to create highly accurate structured mesh around the airoils. In this paper O-type mesh was used and the domain o O-type mesh had a radius o 4 chord lengths to avoid boundary relections; urthermore, ar ield low boundary condition was applied to the border o the domain. The length o the numerical airoil was 1m. Grid contains about 1, cells with around 4 grid points on airoil surace. The height o the irst row o cells around the airoil is set to around.5 o cord length to ensure acceptable value o Y + or utilized SST-Transitional model so that the boundary layer low can be appropriately resolved. In Figure 2 the grids around airoil can be seen. GEOMETRY For Gurney laps, a series o Gurney laps o 1% and 2% o cord length with thickness o.33% o cord length were used at the trailing edge perpendicular to the chord line on the DU 91-W2-25 airoil with geometric parameter as shown in Figure 3. Figure 4 shows the geometric parameters or the trailing edge wedge and the curved shape attached to the trailing edge. H and L are height and length o the trailing edge wedge respectively. In this study dierent L/H ratios (L/H Y/C Curve Wedge X/C Figure 4. DU 91-W2-25 airoil with trailing edge wedge and curve geometric parameters L ratio=length o L/length o H) at two dierent values o 1% and 2% o cord length or H were considered. Furthermore, L/H = 1.5, 2.1 and 3 were used, as depicted in Figure 5 to compare perormance o the curved shape to that o Gurney lap and the trailing edge wedge. For all o the curved shape devices, a curve was obtained rom trial and error or the best perormance o this device. The curve can be expressed by Figure 4. As it can be seen, irst, the longest edge o the wedge H ASME 212 Early Career Technical Journal - Vol