Influence of base inclination on vortex formation during draining from cylindrical tanks

Size: px

Start display at page:

Download "Influence of base inclination on vortex formation during draining from cylindrical tanks"

Harriet Lawson
6 years ago
Views:

1 Indian Journal of Engineering & Materials Sciences Vol. 20, October 2013, pp Influence of base inclination on vortex formation during draining from cylindrical tanks B H L Gowda*, S Akhuli, B R Anudeep, K R Ipe & K Kishore Department of Mechanical Engineering, B T L Institute of Technology, Bommasandra, Hosur Road, Bangalore , India Received 17 September 2012; accepted 13 August 2013 When draining takes place from a cylindrical container, a vortex forms which can affect the rate of draining. This is because the vortex reduces the effective cross-sectional area of the drain port and thus decreasing the flow rate and increasing the time of draining. Experiments show that the presence of rotation augments the vortex formation which is basically due to the low pressure created at the bottom surface. The phenomenon can be expected to be influenced with changes near the base. In this paper the influence of base inclination on the vortex formation is systematically investigated. It is observed that the vortex is completely suppressed when the base inclination is above a limiting value which depends on the size of the drain port. Keywords: Draining from containers, Vortex formation, Base inclination During draining of liquid from a circular tank through an axi-symmetrically placed circular orifice (drain port), a dip forms on the free surface of the liquid which almost instantaneously develops into a vortex with an air core extending to the bottom port. This occurs when the free surface level reaches a critical height, H c, and the vortex extending to the bottom port reduces the effective cross-sectional area of the drain outlet and consequently the flow rate 1-4. The presence of initial rotation can augment the vortex formation, and the flow rate can be further affected 1. Lubin and Springer 5 have studied the axi-symmetric withdrawal of both one and two layer fluids from a circular tank experimentally and analytically. It was observed that the drain rate is nearly constant throughout the draining process until a dip is formed and the critical height is independent of the initial height of the liquid. Steady flow with constant circulation into a vertical drain was investigated by Forbes and Hocking 6. Numerical solutions for the free surface profiles for various conditions are given. The main inference from the investigations is that the draining time is seriously affected by the vortex formation which is augmented by initial rotation. This phenomenon has practical relevance in the fuel feed system in space vehicles and rockets. Due to *Corresponding author ( bhlgowda@yahoo.com) environmental disturbances, rotational motion can be generated in the liquid-propellant tank, which in turn can affect the rate of outflow to the engines. Attempts have been made to suppress vortex formation using different methods. Baffles were used by Abramson et al. 1 to suppress sloshing which also prevented vortex formation. Ramamurti and Tharakan 4 used stepped drain port to arrest vortex formation even with initial rotation present in the liquid column. Gowda 7 has shown that vortex formation can be avoided by using tanks of square and rectangular cross-sections. Gowda et al. 8 used a dish-type suppressor to prevent vortexing. Gowda and Udhayakumar 9 have shown vane-type suppressor to be effective in preventing the vortex formation. Sohn et al. 10 used eccentric drain ports to control vortex formation. In the present study, the influence of base inclination α on the phenomenon of vortex formation and its suppression is brought out. Experimental Procedure The arrangement is very similar to that used by Gowda et al. 8,9 and is shown in Fig. 1 where all dimensions are in mm. An acrylic tank with a internal diameter (D) of 92 mm and height of 460 mm is used with base plates (base inserts) made out of mild steel, having different values of α (Fig. 2 a & b) placed at the bottom to vary the base inclination. One set of

362 INDIAN J. ENG. MATER. SCI., OCTOBER 2013 Table 1 Values of h i for different values of α d = 10 mm α ( ) h i (mm) Fig. 1 Experimental arrangement (all dimensions are in mm) Fig.

2b) had 10 mm drain holes located axially with respect the acrylic tank. The values 92/6 and 92/10 used for tank and drain holes are the typical ratios used in practical applications (e.g.

2 362 INDIAN J. ENG. MATER. SCI., OCTOBER 2013 Table 1 Values of h i for different values of α d = 10 mm α ( ) h i (mm) Fig. 1 Experimental arrangement (all dimensions are in mm) Fig. 2 Inclined base plates (a) base plates with d = 6 mm and (b) base plates with d = 10 mm plates (Fig. 2a) had 6 mm diameter drain holes and the other set (Fig. 2b) had 10 mm drain holes located axially with respect the acrylic tank. The values 92/6 and 92/10 used for tank and drain holes are the typical ratios used in practical applications (e.g. propellant tanks) and are same as used in earlier studies The base inclination achieved with each plate is marked on the plates in Fig. 2. The base plates (inserts) were made carefully to achieve the required α and fitted exactly in the tank. Considerable time and effort was spent in preparing the base inserts. Rotation is imparted to the liquid (water) in the container by controlled stirring (with the drain port closed by a stopper, Fig. 1), using varying number of revolutions of the stirrer over a constant period of time After imparting the rotation, the stopper is removed and draining started. As the draining starts, a dip forms which extends to the drain port almost instantaneously in the form of a vortex with an aircore. The height at which the vortex forms is the critical height, H c. In all the experiments 150 rpm is used for imparting the initial rotation to the liquid in the container. At higher values of rpm, the critical height H c remains nearly constant 7. The initial height of the water (H i ) in the tank was 350 mm and was slightly varied to take care of the volumes taken up by the base plates (due to their thickness) with different α. Table 1 gives the additional height h i of water column for various base inserts with d=10 mm (the values for d=6 mm are nearly same with a difference of 1 or 2 mm). It is known from previous studies that initial height does not influence the vortex formation phenomenon 5. Further, the normalized values of critical height (H c /H i ) and time of draining (t r α / t 0 α ) are plotted. Hence, the additional height of water column added has little influence on the results. The height of 350 mm was chosen so that the critical height could be measured accurately and conveniently similar to

GOWDA et al.: VORTEX FORMATION DURING DRAINING FROM CYLINDRICAL TANKS 363 earlier studies 7-10. Results are obtained for values of α = 2,4,6,8,10,12,14,16,18 and 20 for d=6 mm (Fig.

Results and Discussion All the results with rotation are obtained at 150 rpm (a typical value around which the critical height H c does not vary with rpm 7 ) with D/d = 92/6 and 92/10.

3 GOWDA et al.: VORTEX FORMATION DURING DRAINING FROM CYLINDRICAL TANKS 363 earlier studies Results are obtained for values of α = 2,4,6,8,10,12,14,16,18 and 20 for d=6 mm (Fig. 2a) and α = 2,4 6,8,10,12,14,16,18, 20, 22, 26 and 30 for d=10 mm (Fig. 2b). Results and Discussion All the results with rotation are obtained at 150 rpm (a typical value around which the critical height H c does not vary with rpm 7 ) with D/d = 92/6 and 92/10. These D/d ratios are typical values used in applications. Before conducting the experiments with base inclination and with rotation, the time for emptying the tank with no rotation imparted, for the cases, (i) with different base plates and (ii) without any base plate, was determined and found to be nearly same for both cases. While conducting the experiments due allowance for the additional initial height of liquid necessitated due to the thickness of the various base plate used was provided. The parameter used to assess the influence of the base inclination on the phenomenon of vortex formation is the ratio t rα / t 0α where t r α is the time of emptying with rotation and base inclination and t 0α is the time of emptying without rotation but with base inclination. For each case a minimum of four runs are made for getting the critical height and the time of draining and average taken. The variation in the measurement of critical height is within 5% and the time of draining is within 2% among the different runs. The vortex formation with rotation and draining (d = 10 mm) is shown in Fig. 3. The normalized critical height is shown in Fig. 4 for the cases without and with rotation imparted. The corresponding normalized draining time (t rα / t 0α ) is shown in Fig. 5. In these figures results for both d = 6 mm and d = 10 mm are included. In Fig. 4, the critical height H c refer to the height at which the vortex first appears. However, with base inclination, the following features were observed for both the drain port diameters, d = 6 and 10 mm. At lower values of α, the vortex formed remained till all the liquid was drained. As the value of α increased, the vortex formed initially, started wobbling and becoming thin, thus affecting its capacity to reduce the drain time. With further increase in α, the vortex formed initially, completely disappeared after some draining. However, vortex reappeared (thinner compared to the earlier one) as the draining continued. For example, Fig. 3 Vortex formation with rotation and draining: d = 10 mm

4 364 INDIAN J. ENG. MATER. SCI., OCTOBER 2013 Fig. 4 Influence of base inclination on critical height Fig. 5 Influence of base inclination on draining time

5 GOWDA et al.: VORTEX FORMATION DURING DRAINING FROM CYLINDRICAL TANKS 365 for d = 6 mm and α = 10, the vortex formation occurs at H c = 210 mm and disappears at the liquid height of about 165 mm and reappears at about 160 mm. The draining time is reduced to 80.2 s from 98.5 s, the later being the time of draining with rotation and without the base inclination. For d = 10 mm, α = 14, the vortex formation occurs at H c = 292 mm; it disappears at 285 mm and again appears at 180 mm which disappears at 80 mm. The draining time is reduced to 33.5 s from 51.5 s, the later being the time of draining with rotation and without the base inclination for this case. This appearing and disappearing of vortex occurred several times at higher values of α, e.g., around 18 for d = 6 mm and around 26 for d = 10 mm. After the vortex disappears, there seems to be reorganization of the flow which leads to the formation of vortex again and again. However, the vortex formed under such conditions is seen to be weak and cannot extend to the port area and affect the flow rate. The vortex formation was suppressed at α = 20 for d = 6 mm and at α = 30 for d =10 mm. A dip on the free surface forms at these angles but is not able to extend to the port; it keeps moving on the surface in a random fashion as the draining takes place. The flow features as the draining takes place have been captured by a Videocamera for both d = 6 mm and 10 mm at each value of α. The descriptions of the vortex behavior given in the above paragraphs are clearly seen in the videos at the corresponding value of angle α. Figures 3 (a-d) show photographs (snapshots) of the vortex for different conditions. In Fig. 3a which corresponds to the case without the base insert, a strong vortex with an aircore at the center is seen which extends up to the drain port. It remains till the draining is complete (shown in the video). In Figs 3b and 3c (at α = 14 and 26 ), the vortices formed are in the process of disappearing. At α=30, Fig. 3d, the vortex formation is suppressed. The detailed features as the draining takes place are captured in the videos made at these angles. Figure 4 indicates a sudden drop in critical height at α = 8 for d = 6 mm and at α = 18 for d = 10 mm. However, such sudden variations are not reflected in Fig. 5 for the time of draining. The reasons are possibly due to the appearance and disappearance of the vortex and in some cases it not being able to extend to the drain port as described earlier. These features are seen in the videos at the corresponding angles. Considering d = 10 mm case, it is seen from the video, though the initial vortex formation is occurring at much higher heights from the bottom for α = 18 compared to α = 20, the vortex is weak, disappears and reappears at a lower height. Its influence on time of draining is not much. Hence, in spite of considerable difference in H c / H i (a jump) between α = 18 and α = 20, there is no such large difference in the time of draining. The variation of t rα / t 0α with α shown in Fig. 5 is influenced by the features described above. Also the reasons for the absence of one to one correspondence between Figs 4 and 5 are due to the same reason. For d = 6 mm, the drain time with rotation becomes equal to that without rotation at α = 20, i.e., the vortex formation is effectively suppressed. For d = 10 mm, this occurs at α = 30. However, for d = 10 mm, some marginal effect appears to persist. The probable physical explanation for the effectiveness of the inclined base in suppressing the vortex formation is as: Due to the base inclination, asymmetry occurs at the bottom of the tank because of which the flow towards the central port can be expected to become weaker with α. This will in turn lead to a change in the pressure at the center (near the port). The resulting pressure can be expected to be less negative compared to the case without base inclination. This may be the reason why the dip formed on the free surface when rotation is imparted is not instantaneously pushed down resulting in the formation of a vortex with an aircore extending up to the drain port. To check this loss of symmetry as the base angle increases, some experiments were conducted suspending fine tea dust in the container and imparting the rotation with different base inclinations. The experiments were conducted closing the bottom port, i.e., without draining. The holes in the base inserts were closed by scotch tape. For α = 0 (i.e. without base insert and at small values of α with base insert), when rotation was imparted, a typical vortical flow was created at the centre of the container. When the rotation was stopped, within a short time the tea dust moved towards the axis and collected at the centre of the base in a heap. However, at larger values of α, such movements towards the centre failed to occur after stopping the rotation; there was erratic motions of the tea dust particles indicating absence of symmetry. Further, due to the asymmetry created with base inclination in the fluid body, the

6 366 INDIAN J. ENG. MATER. SCI., OCTOBER 2013 rotation or vorticity introduced is being dissipated much faster, which results in the suppression of the vortex formation. Conclusions It is shown that vortex formation can be suppressed giving an inclination to the container base. However, the details of the phenomenon are found to depend on the D/d ratio. For D/d = 92/6, the suppression occurs at α = 20, whereas for D/d = 92/10, at α = 30. The basic reason for the suppression appears to be the asymmetry introduced into the flow field due to the base inclination. Acknowledgement The authors express their sincere thanks to the Management of BTL IT for their sustained support. Nomenclature D = diameter of the container, mm d = diameter of the drain port, mm H c = critical height of liquid, mm H i = initial height of liquid, mm h i = height of water column to be added to compensate for the volume of the base inserts, mm t o = time of emptying from the axial drain port without rotation, s t oα = time of emptying without rotation with inclined plate of angle α, s t rα = time of emptying with rotation with inclined plate of angle α, s α = base inclination, deg References 1 Abramson H N, Chu W H, Garza L R & Ransleben G E, NASA D-1212 (1962) Pasley G F, J Spacecr Rockets, 18 (1981) Zhou Q N & Graebel W P, J Fluid Mech, 221 (1990) Ramamurthi K & John Tharakan T, J Spacecr Rockets, 30 (1992) Lubin B T & Springer G H, J Fluid Mech, 29 (1967) Forbes L K & Hocking G C, J Fluid Mech, 284 (1995) Gowda B H L, J Spacecr Rockets, 33 (1996) Gowda B H L, Joshy P J & Swarnamani S, J Spacecr Rockets, 33 (1996) Gowda B H L & Udhayakumar H, J Spacecr Rockets, 42 (2005) Sohn C H, Gowda B H L & Ju M G, J Spacecr Rockets, 45 (2008)

Reverse Flow in A Converging Channel with An Obstruction at The Entry - A Flow Visualization Study

14 Reverse Flow in A Converging Channel with An Obstruction at The Entry - A Flow Visualization Study B. H. L. Gowda, BTL Institute of Technology, Department of Mechanical Engineering, Bommasandra, Bengaluru,