AN INVESTIGATION OF CAVITATION PHENOMENONN DUE FLOW PAST OBSTACLES IN CHANNELS

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 13, December 2018, pp , Article ID: IJCIET_09_13_0444 Available online at aeme.com/ijciet/issues.asp?jtype=ijciet&vtype= =9&IType=13 ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed AN INVESTIGATION OF CAVITATION PHENOMENONN DUE FLOW PAST OBSTACLES IN CHANNELS Faten Rashid Al-halidi Eng. at Ministry of Education, Iraq ABSTRACT The movement of fluid flow through bounded or unbounded channel can be found in many practical and industrial applications on a very wide scale. The flow problem of fluids usually subjected to different factors and characteristics that should be involved when dealing with such problems. The flow past an obstacle in a channel produces a phenomenon nown as cavitation. The cavity is a region appears behind the obstacle. This cavity region is of pressure equal to zero, and the study of such region is still needs more studies. The studies require investigating many different factors and problems, and the most important of these problems is that the free surface location of the fluid in its final form, which is usually a major problem and should be computed at first. The investigation of the flow problem is quite complicated in its mathematical equations and also needs algorithms achieve the free surface location within a prescribed acceptable error. The present paper investigates the cavitation and introduces a new numerical solution algorithm. The results due to the present paper are compared with previous results with a very good agreement. Keywords: Cavitation, Stream Function, Types of Obstacles, Boundary Element Method. Cite this Article: Faten Rashid Al-halidi, An Investigation of Cavitation Phenomenon Due Flow Past Obstacles In Channels, International Journal of Civil Engineering and Technology (IJCIET) 9(13), 2018, pp et/issues.asp?jtype=ijciet&vtype=9&itype e=13 1. INTRODUCTION Mechanics are the study of forces and movements, therefore, fluid mechanics is the study of the forces and movements in fluids, but what does the word "fluid" mean? We can all mention clear examples of those fluids (air, water, gasoline, gasoline, lubricating oil and mil). We can also mention some examples that are obviously not fluids such as iron, diamonds, rubber and paper that are classified as solids, but there are other forms of matter such as jelly, peanut butter, mayonnaise, toothpaste, tar and baed dough that have intermediates between fluids and solids [1-5].The ideal fluid is the fluid in which there is no friction or viscosity. It does editor@iaeme.com

An Investigation of Cavitation Phenomenon Due Flow Past Obstacles In Channels not compress and does not exist, in fact, scientists have assumed it and have certain characteristics to facilitate the

In physics there is an ideal fluid, an unreal fluid that does not exist in nature, but is adopted by physicists to facilitate the study of fluids and facilitate calculations with the procedure Some

2 An Investigation of Cavitation Phenomenon Due Flow Past Obstacles In Channels not compress and does not exist, in fact, scientists have assumed it and have certain characteristics to facilitate the study of fluid having the criteria, in-compressible, regular and non-viscous. In physics there is an ideal fluid, an unreal fluid that does not exist in nature, but is adopted by physicists to facilitate the study of fluids and facilitate calculations with the procedure Some changes are in the case of non-ideal fluid, and the ideal fluid is characterized as a non-compressible, non-vortex material, but its flow is uniform[6]. It is also characterized as non-viscous or in other words no friction forces exist between its molecules. A cavity is a zone of steam that occurs behind a fluid-bound collision and occurs in small fluid-free liquid areas, which are the result of the forces acting on the liquid, and also occurs when the liquid undergoes rapid changes in pressure [7-10]. Causing cavities in the fluid where the pressure is low or there is no pressure originally, when these areas are subjected to higher pressure, the blans explode and can generate a severe shoc wave [11].The flow past an obstacle in a channel produces a phenomenon nown as cavitation. The cavity is a region appears behind the obstacle, this cavity region is of pressure equal to zero, and the study of such region is still needs more studies [12-14]. The studies require investigating many different factors and problems, and the most important of these problems is that the free surface location of the fluid in its final form, which is usually a major problem and required determination first. The investigation of the cavity flow problem is quite complicated in its mathematical equations and also needs algorithms achieve the free surface location within a prescribed acceptable error. Cavitating flow are used to replicate a range of natural river flow velocities to determine, the nature of any cavitation damage caused by clear water to roc surfaces under flood durations. In engineering applications, cavitation plays a major role in surface sea-going vessel design and operation, as well as in hydraulic equipment. Propellers, hydrofoil ships, hydraulic turbines and pumps may suffer from its consequences in many ways. Another worldwide application for cavitation is the hydrofoils in navigation or in aerofoils, some of these applications are shown in figure (1). The present paper, investigates the cavitation and introduces a new numerical solution algorithm. The results due to the present paper are compared with previous results with a very good agreement. Figure 1 An experiment of NASA hydrofoil 2. MATHEMATICAL DESCRIPTION AND FORMULATION Consider the movement of a 2-D, fluid flow of the criteria, steady, ir-rotational, incompressible, and the flow will be formulated using Laplace equation [13]: x y = 0, x, y Ω In equation (1), the, represents the potential and it can be re-cast as: (1) = 1 + i (2) editor@iaeme.com

3 Faten Rashid Al-halidi The is defined as the perturbation potential, while is the incident potential. The corresponds to the uni-form in-flow and its magnitude ( xcosβ ysin β ) i = U + Over the free surface, i U at an angle of attac β : (3) i = 0 (4) Where n is the outward unit normal The velocity of the cavity usually ept constant, Q c = U 1 ( 1 + η )2 (5) Derivation the boundary integral equation Start with Green's 2 nd identity, therefore, the B.I. form of equation (1) is [14]: c ( ξ ) ( ξ ) + ( ς ) = Γ Γ ( ξ, ς ) ( ξ, ς ) ( ς ) dγ dγ ( ς ) ( ς ) The is called fundamental solution, mathematically, it taes the following form: 1 = ln( ξ ς ) 2π (7) The fundamental solution defined as the potential at the field point deduced by a unit c ξ given as: charge at a source. In equation (6), the free coefficient ( ) (6) c β 2π ( ξ ) =, 0 c( ξ ) 1 By maing use of discretization technique, equation (6) will be: c Γ = = 1 Ω dω The final boundary integral equation taes the following form: (8) (9) Γ = 1 H i = Γ = 1 G i Q (10) Numerical suggested algorithm Figure (2), represents the new suggested numerical algorithm for tracing the free surface location, based the boundary element method, and stability analysis editor@iaeme.com

4 An Investigation of Cavitation Phenomenon Due Flow Past Obstacles In Channels Figure 2 Flow chart for the new suggested numerical algorithm Numerical Results Figure (3), represents the problem domain with brief details of the fluid flow through a channel and vertical plate as an obstacle. Figure 3 The problem domain editor@iaeme.com

5 Faten Rashid Al-halidi In figure (3): Z The cavity length H The vertical plate length R The maximum location of the F. S. The problem underhand has an analytical solution [1],therefore, the computed results due to the present will be compared with such results so as an achievement of the proposed algorithm will be occurred. Comparison between the results due to the present algorithm and previous available analytical results are in table (1). Table 1 Analytical and computed results z/r R/H q Present Present Anal. Present Anal. z H z/r Anal. R H R/H Fellow up the results due to the present algorithm, figure (3) shows some iterations for tracing the free surface starting from the initial guess, up to the last iteration, for the case of cavity length equals 1.5. Figure 4 The final free surface for three cavity length Then, figure 4 for the same purpose but with cavity length equals 2.5, as it is seen from both fihures, and the previous table one can deduce that the algorithm adopted herein is woring well and promises with excellent results for further applications editor@iaeme.com

6 An Investigation of Cavitation Phenomenon Due Flow Past Obstacles In Channels Figure 5 The final free surface for five cavity lengths. 3. CONCLUSIONS The paper investigated the fluid flow in a channel with a prescribed B. C.,from the investigation, one can conclude the following: A good agreement between the analytical results and the present algorithm. The final form of the free surface has a good agreement with the pghysical behavior expected. The free surface shape, the height and length of the cavity depends on the cavity number. The suggested mathematical model and the numerical algorithm give a promise for further solving more complicated applications. REFERENCES [1] Kinnas, S. A., and Fine, N. E., A numerical non-linear analysis of the flow around 2-D and 3-D partially cavitating hydrofoils, Journal of Fluid Mechanics, Vol. 254,1993, pp [2] Bal, S., A Potential based panel method for 2-D hydrofoils, J. Ocean Eng., Vol.26, 1999, pp [3] Kuiper, G., Cavitation and new blade sections, ASME FED-Cavitation and Gas-Liquid Flow in Fluid Machinery and Devices, Vol.190, [4] Lemonnier, H. and Rowe, A., Another approach in modelling cavitating flows, Journal of Fluid Mechanics, Vol.195, No.2, 1988, pp [5] Dular, M., Bachert, B., Stoffel, B. and Siro, B., Relationship between cavitation structures and cavitation damage, Journal of Wear, Vol.257, 2004, pp editor@iaeme.com

7 Faten Rashid Al-halidi [6] Xie, Z. and He, Y., An approach in modeling cavitating flows with gravity effect, Journal Communications in Nonlinear Science & Numerical Simulation, Vol.2, No.2, 1997, pp , [7] Kinnas, S. A., Lee, H. and Young, Y. L., Boundary element techniques for the prediction of sheet and developed tip vortex cavitation, Electronic Journal of Boundary Elements, Vol. BETEQ 2001, No.2, 2002, pp [8] Kinnas, S. A. and Fine, N. E., A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils, J. Fluid Mech., Vol.254, 1993, pp [9] Ahmed S. G. and Wrobel, L. C., An alternative BEM approach for solving cavity flow problems, International Conference Boundary Element Technology XI, Ertein, R.C. and Brebbia, C. A (editors), Hawaii, USA, [10] Ahmed.S.G., Meshrif S.A., A New Numerical Algorithm for 2-D Moving Boundary Problems using Boundary Element Method', Computers and Mathematics with Applications, Volume 58, Issue 7, October 2009, Pages , [11] S. G. Ahmed et. al., 'Boundary Integral Formulation for Binary Alloys from a Cooling Solid Wall', Journal of Computational and Applied Mathematics, Vol. 5, No. 5, 2010, pp [12] Mohamed H.A.,et al. A collocation mesh-free method based on multiple basis functions, Engineering Analysis with Boundary Elements 36, 2012, [13] Ahmed, S.G. "A new algorithm for moving boundary problems subject to periodic boundary conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 Issue: 1, 2006, pp.18-27, [14] Suyash B.Kamble, Burasei.D., Avinash R.Kharat And Amol A.Nanniar., Modeling The Filling Phase Of Injection Process Of Technical Parts With Thermoplastics Composites Based On Hemp Fibers, International Journal of Mechanical Engineering and Technology (IJMET), 7(4), 2016, editor@iaeme.com

An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies