Flow Visualization of Horton Sphere using a CFD Tool

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ISSN : 2319 – 3182, Volume-2, Issue-1, 2013

101

Flow Visualization of Horton Sphere using a CFD Tool

Lokesh Paradeshi¹, P. G. Tewari² & N. K. S. Rajan³

1Dept. of Mechanical Engg. S.D.M.CLG of Engineering & Technology Dharawad , Karnataka India

2Dept. of Mechanical Engg. B.V.B.CLG of Engineering & Technology Hubli, Karnataka India

3Dept of Aerospace engineering Indian Institute of Science (IIsc) Banglore, India E-mail : [email protected];[email protected];[email protected]

Abstract – Horton spheres are large vessels used in industries like petrochemical, fertilizer, refinery, chemical and power plant to store high pressure or liquefied gas and mix chemicals. Horton spheres are built by a special process. The process of welding induces residual stresses in the material near joints. In order to relieve these stresses, a stress relieving operation is conducted as per standard Flow visualization is one of the more important experimental tools for studying fluid flow and heat transfer. The computational work involves study of flow pattern at Reynolds number of 5.01x10⁵. The grid independence study is carried out in structured mesh and optimum grid size is decided. Different turbulence models that include k-

ε

, k-

ω

and SST are tried out in an industry-standard code (CFX-10) and are compared with experimental results. A study of flow inside sphere is found to be useful in understanding and improving up on the stress-relieving operation of large vessels by optimizing the parameters involved.

Keywords – Horton Sphere, Flow visualization, Computational Fluid Dynamics, Turbulence.

I. INTRODUCTION

Flow visualization is the study of methods to display dynamic behavior in liquids and gases. The areas in which fluid flow plays a role are numerous.

Gaseous flows are studied for development of cars, aircraft and spacecrafts and also for design of machines such as turbines and combustion engines. Liquid flow research is necessary for naval applications such as ship design and is widely used in civil engineering projects such as harbor design and coastal protection. In chemistry, knowledge of fluid flow in reactor tanks is important. In medicine, flow in blood vessels is studied.

Flow plays a major role in cooling of electronic circuits and understanding its complexities help in thermal management of ICs. Numerous other examples could be

mentioned. In all kinds of fluid flow research, visualization is a key issue. Obtaining good flow visualization results is, in many ways, more an art than a science, and experience plays a deciding role. The development of modern techniques for digital image processing of photographic records and use of computers for data analysis has made quantitative measurement by using flow visualization more feasible.

The primary intentions of flow visualization techniques are to acquire the following observations and measurements:

 A streak line, path line and/or a streamline all of which show flow direction.

 Flow velocity, its gradient and/or acceleration and the corresponding distributions.

 Density and temperature distributions of a fluid

 Location of shock waves mainly in passages such as nozzles and in external flow such as over aerofoil.

One way to understand flow is to perform experiments. Until recently experimental flow visualization has been the main visualization aid in fluid flow research. Experimental flow visualization techniques are applied for several reasons:

Recently a new type of visualization has emerged:

computer-aided visualization. The steadily increasing performance of computers has become a driving factor for a new boom in flow visualization [1]^*. Computer based flow visualization can provide a quick, qualitative and quantitative assessment of a new flow field, guiding initial concepts and design of more detailed experiments In practice, often both experimental and computer- aided visualization will be applied. Fluid flow visualization using computer graphics will be inspired by experimental visualization.

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102 II. HORTON SPHERE

Horton spheres are large vessels used in industries like petrochemical, fertilizer, refinery, chemical and power plant to store high pressure or liquefied gas and mix chemicals. The pressure vessel of spherical configuration provides a lightweight design, which has a two to one stress advantage in hoop stress over a cylinder with same wall thickness and internal pressure.

Sphere also has advantages of lower weight to volume ratio of shell for pressurized storage, larger capacity, minimal corrosion and less risk of oxygen ignition and explosion. The diameter of sphere varies from 10m to 20m and total weight of system is about 350 tonne.

Assuming quite a heavy wall spherical pressure vessel of large dimensions, material and thickness of plates is selected depending upon service pressure and conditions. The materials used for this product are carbon steel, stainless steel and low alloy steel. Horton spheres are built by a special process. The spheres are made up of a large number of pieces called petals obtained by pressing sheet metal at factory site. These pieces are transported to field where they are assembled into spherical shape and joined by welding. The process of welding induces residual stresses in the material near joints. In order to relieve these stresses, a stress relieving operation is conducted as per standard ASME codes.

The stress relieving operation amounts to heating the sphere at a rate not exceeding certain limit and soaking it at temperatures between 873 K and 1023 K depending on material also governed by ASME code for specific duration. It is required that at soaking, temperature difference over the sphere should be no more than +/- 20 K. At relatively small size of vessel stress-relieving operations is performed by introducing vessel into a furnace. At sizes of 1 to 20 m in diameter this procedure turns out to be impractical. Hence in this case a burner is used to introduce hot gases into the sphere to heat the vessel and covering outside with insulation that helps in conserving heat as well as making heat flow more uniform.

Horton sphere and There are two openings one at the bottom and another at the top. The dotted lines indicate petals, which are developed and hot pressed at factory into segments of the sphere for the purpose of fabrication at site. The thickness of vessel varies between 20-45 mm in most applications. The welded joints are radio-graphically tested for homogeneity of weld and then the vessel is subjected to heat treatment to relieve stresses induced during welding. To provide heat treatment at site, sphere is provided with insulation, typically with mineral wool of 75-100 mm thickness and a burner specially designed for this purpose is used to carry out stress relieving.

III. MODELLING AND MESH GENERATION A. Geometric modeling : The geometric modeling of sphere in Ansys workbench 10.0 was done on same grounds as in experimental study as shown in fig1.

Since flow in sphere is axis-symmetric it was not necessary to solve flow for entire sphere. The simulation done on a section of sphere would imply to the whole domain. So a half of sphere was built in Ansys workbench 10.0 and simulations carried out using that.

A half of sphere of 336 mm diameter was built with inlet and outlet ports of 9 mm diameter.

Fig. 1: Geometry Modeling in ANSYS Work bench 10 B. Parameter taken for study : Diameter of the Sphere

= 336mm; Diameter of the inlet and out let tube = 9mm.

Density of water, ρ = 1000 kg/m³, Dynamic viscosity of water, μ = 0.001 N-s/m² Mass flow rate, at inlet and outlet Q = 0.0945kg/s (Experimental measured values) Q = ρA V (kg/s)

V = Q/ρA = 0.0945/ (1000*π/4*(0.009)² Reynolds number,

R_e= 1000 * 1.4845*0.336/0.001 = 5.01* 10⁵

C. Meshing: The model can be meshed into structured grid. In structured grid there is some type of consistent

V= 1.4845m/s

* *

e

R  V D

 

Re = 5.01 * 10⁵

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103 geometrical regularity. Using Ansys ICEM CFD as shown in Fig.2. and mesh is generated. The mesh has been clustered more at wall of the sphere to capture boundary layer growth near the wall. And the following parameters are used for the computational analysis Table I gives the parameters for which computational study is conducted.

Fig. 2: Model meshed in ICEM CFD 10.0 Structure Mesh

TABLE I

Mesh parameters for which computational study is conducted

SL.

NO NO OF NODES ALONG RADIA L EDGE DIRECT

ION

TOTAL NO OF NODES

TOTAL NO OF ELEME NTS

NO OF HEXAH EDRA ELEME NTS

REYNOL DS NUMBER

FLOW MODELS

1 12 50000 53595 48799 1660 2110 21000 3 x 10⁵ 5 x 10⁵

Laminar k-

ω

k-

ε

SST 2 28 100000 102770 91230

3 45 150000 154670 141814 4 60 200000 205845 190249 5 80 250000 256745 236829 6 100 300000 308645 293409

IV. COMPUTATIONAL APPROACH

The Reynolds–Averaged Navier–Stokes (RANS) Equations are solved for steady, single–phase, incompressible and viscous flow. For all the computations, fluid considered is water with constant fluid properties.

The continuity equation:

The momentum equation:

The energy equation:

V. RESULTS

A. Flow pattern: A clear picture of nature of flow inside sphere as obtained from computational study is shown in Figs 3. These figures give streamline and vector plots respectively for 5 x 10⁵ Reynolds number at 2.0 lakhs nodes and k- ω model. Computational flow pattern is acceptable, as experimental flow pattern is in close agreement with it as viewed in visuals.

The flow in sphere consists of two structures; one of the center-line jet entraining the fluid and moving upwards and another having toroidal vortices due to a recirculating zone.

The longer tracks imply higher velocities. The two dominant toroidal structures indicating a recirculation zones are located axis-symmetrically in a plane. The eye of vortex is located in upper half of the sphere slightly above the diameter that cuts sphere into two halves in horizontal plane perpendicular to plane of vision. The flow velocity is very low in recirculating zone. The centerline jet expansion can be observed in the figure.

The velocity drops along axis to about 87% of injection velocity at the center of sphere and increases back to near injection velocity at the exit. The velocities in the 5 O’clock and 7 O’clock regions are very low.

Fig. 3: Streamline & Vector plot for Re = 5 x 10⁵ of k- ω model

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104 B. Grid refinement study: To study variation of flow with change in grid size, grid independence study was carried out. This was done for higher Reynolds number of 5 x 10⁵ because if flow structure remains same with increase in number of nodes for higher Reynolds number then flow at lower Reynolds number is automatically taken care of. Grid refinement was done from a grid size having 50000 nodes to that having 3.0 lakh nodes, the intermediate grid size being 1.0 lakh , 1.5 lakh , 2.0 lakh, and 2.5 lakh nodes. In discussions, flow of 5 x 10⁵Reynolds number with k-ω model is considered. Fig. 6 and 7 shows streamline plots and vector plots for different grid sizes respectively.

Boundary layer growth is better captured for higher grid size. There is a large variation in both axial and radial velocities between the lowest and the highest grid size as can be seen from Figs. 4 and 5 Starting from 50000 nodes, variation of axial velocity at center of sphere, for specified nodes, as compared to the respective next highest nodes are 7.7%, 1.9%, 1.3%, 0.5% and 0.2% {Fig.4.} and those for radial velocity near the wall of sphere are 92%, 7.3%, 5.4%, 1.2 %and 0.5% {Fig.5.}. Hence it can be seen that variations in velocities decrease as grid size increases and it is minimal between grid size of 2.0 lakh nodes and 2.5 lakh nodes.

From the grid independence study, it can be observed that grid size with 2.0 lakh nodes, with more clustering near wall of sphere, to be optimum to predict flow in sphere with greater accuracy

Fig.4: Comparison of axial velocity for different grid size

Fig. 5: Comparison of radial velocity for different grid size

Fig. 6 : Streamline plots for different grid size

(d) 2.0 lakh (e) 2.5 lakh (f) 3.0 lakh (f) 3.0 lakh Nodes

(a) 0.50 lakh (b) 1.0 lakh (c) 1.50 lakh

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105

(a) 0.50 lakh (b) 1.0 lakh (c) 1.5

Fig. 7: Vector plots for different grid sizes C. Flow mapping of Experimental results with

computational:

This section presents a brief description of flow pattern obtained from the same model using different turbulent schemes like k-ω, k-ε, SST-models using CFX-10 and their comparison with experimental results.

In all the CFD analysis used for different models (k-ω, k-ε, SST-models), for the common basis for comparison dimensional similarity and same boundary conditions such as similar mass flow rate is maintained as per the experimental values.

Comparison with k-ε model Fig.8. Shows the comparison of the Experimental Streamline plots with Computational streamline plots using k- ε model.

Comparison with k- ω model Fig.9. Shows the comparison of the Experimental Streamline plots with Computational streamline plots using k- ω model.

Comparison with SST model Fig.10. Shows the comparison of the Experimental Streamline plots with Computational streamline plots using SST model

Fig. 8: Comparision of Experimental results with computation results

(Stream line plots, m^. = 0.0945 kg/s, k-ε-model)

Fig. 9 : Comparision of Experimental results with computation results

(Stream line plots, m^. = 0.0945 kg/s, k-ω-model)

Fig.10 : Comparision of Experimental results with computation results

(Stream line plots, m^. = 0.0945 kg/s, SST-model) (d) 2.0 lakh (e) 2.5 lakh (f) 3.0

lakh

(f) 3.0 lakh Nodes

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106 VI . CONCLUSION

The data obtained from the analysis agreed within 5% differences in most of the regions, except near the inlet (in main jet stream, from the injection point to about a distance of about one third of the sphere diameter on the axis) where the differences were of the order of 10-15% in the range of measurements. These differences near the inlet were due to fact that the velocity gradients being high, it was difficult to know whether a particle being tracked was entrained or resident in the main stream while mapping the tracks of the Particle. Experimental results are in close resemblance with k-ω model (in comparison with other two models k-ω and SST-models) within 5-10%

differences in most of the regions. Thus Experimental results validate the use k-ω model. And the measurements have given the velocity profiles through the sphere.

The results obtained from the experiments are found to be in close agreement with the CFX results using k-ω turbulent model as against k-ε, SST-models.

This indicates that the validation qualifies the usage of the k-ω model as the effective turbulent scheme in the CFD model for the further heat transfer studies carried out in these geometries.

VII. REFERENCES

[1] Rajan N. K. S., “Experimental and Computational Studies of Fluid Dynamics and Heat Transfer in Spherical Vessels”, PhD Thesis, Department of Aerospace Engineering, Indian Institute of Science, 1989

[2] Rajan N. K. S., Mukunda H. S., Paul P. J.,

“Internal Flow with Free Convection in Large Spherical Vessels - Computation and Experiments” Department of Aerospace Engineering, Indian Institute of Science, Bangalore.

[3] Mukunda H. S., Raghunandan B. N., Rajan N. K.

S, Paul P. J., “High Velocity Burners And Stress-Relieving Of Horton Spheres”, Internal Report, Dept. of Aerospace Engineering., Indian Institute of Science, 1985.

[4] Tara herle.p., experimental and computational analysis of fluid dynamics in horton sphere.tech thesis, department of energy systems engineering, bvb college of engineering & technology,hubli, 2004-2005.

[5] Tsuyoshi Asanuma, “Flow Visualization Techniques in Japan”, Proceedings of International Symposium on Flow Visualization, October 1977, Tokyo, Japan, pg 3-4.

[6] http://www.ansys.com/products/cfx.asp#, Master Contents of software CFX-10.

[7] John D. Anderson, Jr., “Computational Fluid Dynamics: Basics with Applications”, Mcgraw- Hill Inc., 1995, pg 4-11.

[8] Versteeg H,Malalasekera W., “An Introduction to Computational Fluid Dynamics: Finite Volume Method”, Longman Scientific & Technical,1995, pg 1-2.

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