Experimental and Numerical Studyof Circular Hydraulic Jump on a flatplate

by Rohan Sharma (100100068)

Supervisors:

Prof Arunkumar Sridharan

Prof Amitabh Bhattacharya

1

Outline• Introduction• Objective• Literature Review• Experimental Study• Numerical Study• Conclusions and future work

2

Introduction• Hydraulic jump is marked by sudden rise in downstream

fluid depth when fluid speed changes from supercritical to subcritical

• Phenomenon first observed in planar flow; cases such as river bore studied extensively

• Circular Hydraulic Jump (CHJ) occurs when fluid jet impinges a solid obstacle creating a stagnation zone at the center

3

Circular Hydraulic Jump

4

Introduction• CHJ produces extremely high heat transfer coefficients

and hence has vital applications in the field of local dissipation

• The heat transfer coefficient falls drastically downstream of the jump, hence finding the jump radius is the priority

• Although, solutions for horizontal plate are readily available, data for inclined plate is scarce

5

Objective• To study the physical characteristic of CHJ through

experiments and numerical simulations• To develop a physical explanation for hydraulic jump using the

viscous theory• To carry out unprecedented experiments for the case of

inclined flat plate• To develop an accurate numerical solution for the problem• Utilize the results obtained to augment the accuracy of heat

transfer approximations

6

Literature Review: Analytical Study

• A complete solution, which gives the jump radius just on the basis of input jet characterisitics, is still elusive

• Various models, experimental and analytical, try to solve for jump radius, albeit, using at least one additional parameter such as downstream depth or flow profile

• Notable work has been done by Liu and Lienhard [1], Watson [2], Bohr [3], and Bush and Aristoff [4]

• We look at the salient points of aforementioned theories and experiments

7

Analytical Study• Liu and Lienhard conducted experiments to study the

structure of CHJ• Presence of separation eddies was observed in the core jump

region• Jump radius was seen to behave in the following way

• increases with increase in flow rate of the fluid• decreases with increase in downstream height of the obstacle• decreases with increase in surface tension of the fluid• decreases with increase in viscosity of the fluid• decreases with increase in gravitational force• does not depend on nozzle height

8

Analytical Study

a) Smooth jump

b) Single roller jump

c) Double roller jump

d) Unstable jump

Based on the structure, CHJ is divided into four types

9

Analytical Study• Watson used boundary layer theory to solve the CHJ

problem analytically; he obtained an analytical relation for jump radius based on known downstream depth

• The flow was divided into different region which were solved separately assuming different velocity profiles

10

Analytical Study• This model didn’t include surface tension and hence

failed in the cases where the jump depth was small• Bush and Aristoff modified Watson’s theory by adding

surface tension to obtain improved results

11

Literature Review: Numerical Study

• Navier-Stokes equation for two-dimensions is solved• Presence of two different fluids calls for a new algorithm;

two salient methods for interface tracking are• Front Tracking• Volume of Fluid (VOF) method

• VOF method has been preferred because• It naturally conserves the mass of each phase• Global topology changes are handled automatically• VOF method is known to have a relatively faster

convergence rate when a large number of cells are used

12

Numerical Study• A color function, F, is defined for each cell, whose value

represents the volume fraction of heavier fluid (referred as liquid from here on) in that cell

• This value is updated with time by the advection equation

• Based on the F values, interface is reconstructed using Youngs’ PLIC method [5]

• Surface tension is then calculated as a body force term as done by Brackbill [6] in his Continuum surface force model; modifications suggested by Williams are deployed [7]

13

Numerical Study: Interface Reconstruction

14

Present Work

15

Experimental Results• Experiments are conducted for the case of horizontal

plate and inclined plate; former was done to check the robustness of the setup

• The jump radius and the profile was studied by varying following parameters• Nozzle Diameter• Jet Reynolds number• Nozzle to plate spacing

16

Experiments: Flat Plate• Reynolds number has been varied between 15,000 and

30,000• two different nozzles of inner diameters 8.8 mm and 6.6

mm are used• Five different nozzle to plate spacing between 10 mm

and 50 mm are used• The results obtained are compared to that of Rao and

Arakeri [8] and Liu and Lienhard• Maximum deviation was observed to be around 20 % for

the case of unsteady jump

17

Experiments: Flat Plate

Formation of circular hydraulic jump on a at plate for Reynolds number23,000 and Jet diameter 8.8 mm

18

Results: Flat Plate

19

Experiments: Inclined Plate• Reynolds number has been varied between 3,000 and

13,000• Two different nozzles with inner diameter 4 mm and 6

mm have been used; • Nozzle to jet spacing varies between 10 mm and 30 mm• Four different inclination angles between 10o and 45o

have been used

20

Experiments: Inclined PlateExperimental setup for inclined plate; angle of inclination in this case is 20 degrees

Pacman-esque jump pattern is observed for 20 degrees inclination

21

Results: Inclined PlateVariation in jump profile with inclination and nozzle to jet spacing for Nozzle diameter 4mm. a) Re=2000, θ= 20o; b) Re=3000, θ= 20o; c) Re=3000, θ= 30o d) Re=4000, θ= 30o; e) Re=3000, θ= 45o; f) Re=4000, θ= 45o

22

Results: Inclined Plate

23

Numerical Simulation: Flat Plate

• ANSYS-FLUENT has been used to corroborate the experimental data

• The result for flat plate with an obstacle are first compared to that of Fard [9] and then independent simulation for the experimental case is carried out

• FLUENT uses an algorithm similar to VOF; surface tension is modelled using Brackbill’s CSF method

• SIMPLE is used to solve the velocity equation; PRESTO is used for pressure equation

• For the case of infinite plate, to speed up the convergence, an initial depth of 2 mm is used

24

Numerical Simulation: Flat Plate

Computational domain showing different boundary conditions used; Uniform grid is used as it is favorable for VOF computation

25

Results: Flat PlateVariation of jump radius with time for an external obstacle of height 2 mmFlow rate= 30 ml/sJet Radius= 5mm

26

Numerical Simulation: Validation

Validation of jump radius obtained with that obtained by Fard for an obstacleof size 2 mm

27

Numerical Simulation: Validation

Comparison of data obtained by experiments and Numerical Simulation using ANSYS

28

Numerical Simulation: VOF• The results obtained using ANSYS tends to deviate from

the original values• Fard attributes this to incorrect surface tension

modelling; ANSYS uses Brackbill’s CSF model which is of first order accuracy

• This can be corrected by using a better approximation for surface tension given by Williams

• An indigenous code has been written using MATLAB which uses Williams’ model for surface tension modelling

• The case of a drop falling in another medium has been validated with that of Tryggvason [10]

29

Numerical Study: Algorithm

30

Numerical Simulation: VOF• A square staggered grid with dimensions 1 cm x 1 cm is

used• The computational domain is divided into Nx and Ny

pressure centers• The density of bubble is 2 kg/m3 and density of the

medium is 1 kg/m3

• Fall of the bubble with initial radius 15 mm is observed and compared with that of Tryggvason for a fall time of 0.00125 s

31

Numerical Simulation: VOF

Staggered Grid used for MATLAB code

32

Results: VOF

Capturing free fall of a drop in a viscous medium; a) The modified interface obtained using VOF methodb)Simulation done Tryggvason, Front tracking solver for Navier-Stokes equation, deploying DNS scheme

33

Conclusions• Experimental study has been carried out for hydraulic

jump and following points can be made regarding the jump radius for horizontal flat plate• Jump Radius increases with increase in flow rate of the fluid• Jump Radius does not depend on nozzle height• Jump Radius increases with nozzle diameter

• For the case of inclined surface, a departure from axisymmetry is observed and

• The jump takes a pacman-esque shape.

34

Conclusions• Following can be commented about the shape feature

• The distance between the apex and center of the jump increases with increase in flow rate

• The distance between the apex and center decreases with increase in inclination

• The distance between the apex and center is invariant with nozzle height

• Numerical Validation for the flat plate was achieved using ANSYS-FLUENT

• Results weren’t as robust for the inclined plate• This can be attributed to improper surface tension

modelling as pointed out by Fard35

Future Work• Modify the VOF code to solve the CHJ problem for

horizontal and inclined flat plate impingement• Experiments will be conducted for studying heat transfer

characteristic of circular hydraulic jump on horizontal and inclined surface

• Modification of the code developed to validate the results thus obtained.

36

References

37