Simulation and improvement of the ventilation of a welding workshop using a Finite volume scheme code

Transcription

1 1 st. Annual (National) Conference on Industrial Ventilation-IVC2010 Feb 24-25, 2010, Sharif University of Technology, Tehran, Iran IVC2010 Simulation and improvement of the ventilation of a welding workshop using a Finite volume scheme code Mani Mahdinia M.Sc. Student Mahdinia@mech.sharif.edu Amir Ghasemi M.Sc. Student AGhasemy.v@gmail.com Bijan Farhanieh Professor bfia@sharif.edu Sharif University of Technology, Mechanical Engineering School, Tehran,Iran Abstract A Finite-volume CFD code is developed for the solution of the Navier-Stokes equations in an industrial ventilation domain. The point at the middle of the domain, having a temperature of 500 C, is the place where a welding process is being accomplished. Due to the high temperatures at the vicinity, three fans (one supply and two exhausts) are used. The purpose of this study is to investigate the effect of different parameters on the local ventilation and developing the most effective ventilation scheme for this applied problem. In order to find the velocity components and the temperatures, the equations are solved in a Cartesian coordinate system and a collocated grid. To prevent the checkerboard distribution, velocity components on the faces of the control volumes are obtained by the Rhie and Chow interpolation scheme. SIMPLE algorithm is used for the modeling of the pressure-velocity coupling. Convection fluxes have been discretised, using the upwind scheme and the resulting equations have been transformed into a tri-diagonal matrix with the use of the ADI technique and solved with the Tomas Tridiagonal algorithm. For the sake of maximum accuracy, the grid has been refined at the points of larger velocity gradients. The developed code accuracy has been verified against the cavity flow test case and checked for the grid independency. The effect of different variables like the wall lengths, boundary conditions and flow rates has been studied. Using all the above mentioned techniques and results, an effective ventilation scheme has been proposed for the ventilation of the welding stand. Keywords: Industrial Ventilation, Computational Fluid Dynamics, SIMPLE Algorithm, Quick Scheme, Rhie- Chow Interpolation Scheme 1) Introduction The improvements in the industrial technologies, has lead to a growing need for the more carefully designed and manipulated methods of ventilation. This includes manufacturing industries like car production factories, subway environment ventilation, clean room HVAC and so many others. Amongst these diverse applications, those that involve higher temperatures, like the one in an industrial welding stand may need more attention and care. The temperature in the vicinity of a welding point may become as high as 1000 degrees Celsius, which may result in an enormous temperature rise due to the accumulation of the generated heat, leading to an uncomfortable or even harmful environment for the workers, if not properly cooled. Since different cases of industrial ventilations, involve many kinds of flow configurations and geometries, it is nearly impossible to rely completely on the experimental methods. Regarding this fact, other tools such as Computational Fluid Dynamics techniques, have gained more attention in this field, specifically in the recent decades, thanks to the improvements in the computer technology. Another beneficial factor regarding the CFD methods is that it enables one to analyze the performance of the designed ventilation system for various arrangement and parameters and also select the best. To achieve such an optimization using an experimental approach may demand a huge amount of resources, even if it is possible. The problem at hand pertains to the cooling and ventilation of a welding stand, used in the car manufacturing industries. The geometry of the problem is shown in Fig. (1). A welding process is being accomplished in the middle of the domain and the three surrounding internal walls isolates the welder from its surroundings. The article organization is as follows. After this brief introduction, the governing equations and the boundary conditions are derived for the problem at hand. Then the discretization method and the numerical solution algorithm are investigated in detail. After this part, the code accuracy verification is accomplished by testing its results for the well-known cavity flow. In the next section, the grid independency of the results is investigated. Finally, the simulation results are presented and the effect of various parameters is taken into consideration. The effect of the inlet and outlet relative velocities and Reynolds numbers has been determined. Also the impact of the type of the outer B.C., considering the symmetry, wall and free boundary condition types has been investigated. Other geometrical parameters like the length and location of the internal walls, the size and location of the fans and the welding point position has also been studied. Finally, the effect of the variance of the fluid properties like the Prandtl number due to the temperature changes was determined. Using these results, the best possible configuration amongst the ones considered is chosen for the applied use. This arrangement may result in the best efficiency of the equipment.

2 equations are solved in the left half of the domain. The boundary conditions of the flow are shown in Fig.2. The right boundary (No. 7) is considered to be a symmetry line as stated above. The lower boundary (No. 3) is an impermeable wall with no slip conditions for velocity and zero-flux condition for heat. The outer edges (No. 4) are considered as free boundaries with zero heat flux, based on the assumption that the changes of temperature in the vicinity of these boundaries are negligible relative to the middle point of the domain. The No. 1 and No. 2 boundaries are considered as inlet and outlet boundaries (constant velocity) respectively, with a prescribed temperature in the inlet and an extrapolated temperature for the outlet. For the internal walls (No.6), a no slip condition on velocity and a convective condition for temperature are imposed. Fig 1 - Computational domain of the problem 2) Governing Equations The air flow is assumed to be incompressible, twodimensional and steady. The continuity, x and y momentum and the energy equation for the assumed conditions are + =0 (1) + = 1 + ( + ) (2) + = 1 + ( + ) (3) ( + )= ( + ) (4) It should be mentioned that due to the low velocities in the solution domain, the dissipation in the energy equation (4) has been neglected. To handle the flow problem in a more general fashion, the equations have been non-dimensionalized, by using the following definitions =, =, =, =, = Substituting (5) in (1) to (4) gives (5) + =0 (6) + = + 1 ( + ) (7) + = + 1 ( + ) (8) ( + )=. ( + ) (9) In which the Reynolds and Prandtl numbers are defined as = and =. In the next sections, the star superscripts on the variables are dropped for ready reference. 3) Boundary conditions To reduce the computational cost of the solution, the Fig 2 - Boundary conditions of the domain 4) Solution algorithm Equations (6) to (9) are discretised using the finite volume method, on a collocated grid. Such a grid is based on storing the velocities and pressures in the same locations in the mesh, which is in contrast to the commonly used staggered grid. Incorporating the collocated grid has the advantages of having a lower amount of storage required and also the ease of programming. Its disadvantage is that it may lead to a checker-board pressure distribution in the domain. To overcome such a problem, the Rhie-Chow interpolation scheme [1] has been incorporated to evaluate the volumetric fluxes on the cell surfaces. For the pressure-velocity coupling, the SIMPLE [2] algorithm has been used. To find the quantities on the surfaces of the control volumes, the Upwind method has been used. Using the above mentioned algorithms and techniques, results in a linear system of equations, which have been transformed into a tri-diagonal matrix with the use of the ADI technique and solved with the Tomas Tridiagonal algorithm. For the sake of maximum accuracy, the grid has been refined at the points of larger velocity gradients. A C++ code is developed to implement the mentioned solution process.

3 5) Code verification The developed code has been verified against the wellknown test case of the cavity flow. The geometry of the flow is shown in Fig. 3. In the figure, the side and bottom walls are stationary and the no slip condition is imposed on them. The top boundary on the other hand, is moving with a constant velocity of 1 m/s to the right. The x-velocity profiles on the vertical middle line of the geometry, i.e. =0.5, have been verified with the experimental results of the well-known work of Ghia et. al.[3] and shown in Fig. 5, for the two Reynolds numbers. Fig 3 Geometry of the cavity flow The domain has been discretised using a grid for the Reynolds number of 400 and a grid for the Reynolds number of To show the flow configuration more clearly, the streamlines are shown in Fig. 4, for both of the Reynolds numbers. Fig 5 - x-velocity profiles on = 0.5 line Re=400 Re=1000 Fig 4 - Streamlines Re=400 Re=1000 (with the definition Re=uL x /ν) As can be seen, the results of the simulation are in good agreement with the experimental results. The y-velocity profiles also agree with the empirical data in a similar manner, but to save space the results have not been presented here. 5) Grid independency A structured grid has been used to transform the PDE equations to a set of linear algebraic equations. To achieve an acceptable level of accuracy and also to avoid unnecessarily high computational costs, the five cases of different grid sizes have been considered; , , , and The results for the x-velocity on the = 4.8 line and y- velocity on = 1.2 line (based on the coordinate system origin at the lower left corner of Fig. 1) have been compared for the stated grid sizes, in Fig. 6 and Fig. 6 respectively. As illustrated in the figure, the meshes more refined than the size of , collapse

4 Fig 6 - Grid independency results x-velocity on the = 4.8 line y-velocity on = 1.2 line together. So we choose this mesh size as our basic grid size. To achieve the final maximum accuracy, the grid is refined in the places where high gradients of the velocity are expected, as shown in Fig. 7. 6) Simulation results The velocity variables are nondimensionalized with respect to the inlet velocity so the inlet velocity has been assumed to have a value of 1m/s. Inlet Reynolds number of 200, which is defined, based on the characteristic length of H has been considered. The outlet velocity is calculated based on the ratio of the inlet Reynolds number to that of the outlet (outlet Reynolds number is equal to 80). Flow streamlines and temperature Contours are shown in Fig. 8. and Fig. 9, respectively. As can been seen, two large kidney-shaped circulating flow regions are formed between the internal walls as a result of flow entrapment between them which also prevents effective ventilation. Another point is that according to Fig. 8, the flow has the ability to travel into and out of the domain, due to assumption of the free boundary for the outer edges. Also, since the net outflow of the inlets and outlets together are a negative quantity, the net flow on the outer edges (excluding the inlets and outlets) should be towards the outside of the domain. This forces the streamlines to become denser near the outlets of the Fig 7 - Grid refinement Basic grid locally refined grid refined Fig 8 - Flow streamlines domain. The temperature contours are shown in Fig.9. As can be seen from the figure, the constant temperature lines are perpendicular to the lower wall, in accordance with the insulated B.C. assumption. Also, gradient, far

5 the ambient temperature, i.e. larger distance results in the loss of the flow velocity at the boundaries, without any benefits. Fig 9 - Temperature contour from the welding point. Also there exists a for the side free boundaries show the same behavior, which confirms our prediction of negligible temperature large temperature gradient near the center of the domain, exhibiting effects of the ventilation near the point. 7) Effect of parameters In this section, the effect of various parameters on the flow field is investigated in order to reach at the best possible configuration for the system at hand. 7-1) Boundary conditions Here, three various configurations are considered: The welding stations are positioned in an array, having a large distance apart. This gives us the free boundary condition. The same as previous, but the distances are small so that the symmetry B.C. is applicable. (c) Each welding station is separated from the surrounding using partitions. This results in wall B.C. The flow stream lines and temperature contours are demonstrated in Fig. 10. The differences between the streamlines in parts to (c) is largely due to the large vortices at the top corners of the domain, which result from flow area expansion in the and (c) cases. In case, the flow entrance from the upper boundary and its exhaust from the vertical boundaries, prevents the formation of any large vortices. The temperature contours show a larger temperature for the case of the free boundary. This is due to the outflow of a large amount of the current before getting close enough to the welding point. Amongst the two other configurations the symmetry boundary, which stands for a small-distance array of welding stands in a workshop, gives a lower temperature distribution in the domain. This is in contrast to the no-slip boundary conditions in the case of the wall boundaries (a partition-separated array), that slows down the flow around the welding point, that lowers the effect of the ventilation. These results suggest using an array of stands in the welding workshop, where the stands are positioned in a way that the minimum distance between them is chosen so that the temperature at the boundary just reaches 7-2) Inlet and outlet Reynolds numbers The effects of the changes of the inlet and outlet boundary conditions are shown in Fig. 11. The main case is repeated for ease of comparison. Cases and (c) represent the configurations in which the inlet and outlet Reynolds numbers are the same and are equal to 80 and 20 respectively. In case the equivalence of the inlet and outlet Reynolds numbers, reduces the tendency of the current to cross the boundaries of the domain, which moves the flow towards the formation of circulating vortexes in the domain corners. In case (c) the lowered Reynolds numbers in the inlet and outlet, results in a streamline pattern which interestingly resembles the creeping flow, where the flow lines smoothly turns around the obstacles without separation. The reduction of the Reynolds number from case to and from to (c) results in the shrinkage of the vortexes amongst the internal walls, in such a way that the big vortex in breaks down into two smaller vortices in and finally at (c) it diminishes to a very small size. The velocity reduction in the flow domain results in an increased magnitude of the temperatures in cases and (c). 7-3) Internal wall configuration Regarding the internal wall configuration, one may consider attaching the walls together to prevent harmful effects of the radiation to the surrounding people, but unfortunately this feature may prevent the effective ventilation as well. This conflict motivates us to investigate this parameter. The velocity vectors and temperature contours in the domain, in such a configuration is shown in Fig. 12. As can be seen, the velocity magnitude decreases in the middle region and the current is entrapped between the walls, as was expected, which results in the diminution of the convection cooling and causes in the temperature rise in the vicinity of the welding point from 320 C in Fig. 10 part (aʹ) to 400 C in Fig. 12 part. Since the temperature difference in the two circumstances is too large, the idea of attaching the walls, may not work as a proper solution and we have to look for other methods to circumvent the radiation hazard. 7-4) Dependence on the Prandtl number The analysis here may become subjected to several variations in the parameters. The uncertainty in the parameters can be due to the seasonal temperature changes. Here we investigate the effect of the variation of the Prandtl number in the equations. The temperature contours for two different Prandtl numbers are shown in Fig. 13. As can be seen the lower Prandtl number results in the penetration of the high temperatures in a bigger region in the domain.

6 (c) (aʹ) (bʹ) (cʹ) Fig Effect of different boundary conditions to (c) Streamlines for the free, symmetry and wall B.C.s and (aʹ) to (cʹ) Related temperature contours (c) (aʹ) (bʹ) (cʹ) Fig Effect of inlet and outlet Reynolds numbers to (c) Streamlines with Rein=200, Reout=80 Rein=80, Reout=80 (c) Rein=20, Reout=20 - (aʹ) to (cʹ) Related temperature contours

7 Fig 12 - Effect of the internal wall configuration Velocity contours Temperature contour 8) Conclusions A finite volume CFD code has been developed for the simulation of the ventilation of a welding environment. Since the welding configuration considered in this study is a common installment in many welding stands, its study and optimization may be of a general interest. We have used this code as a means for a virtual laboratory to investigate the effect of various parameters on the function of the system. Decision about the position of welding stands relative to each other, i.e. being separated through partitions or being in near or large distances from each other, can be subjected to several parameters in which the effective ventilation may contribute as a most important parameter. To investigate this issue, the flow has been simulated using three different configurations and it has been found that being apart through partitions can be the best arrangement, which would be hard to identify before the numerical simulation. Upon considering the results of sections 7-2 and 7-3, in order to have a better cooling one has to use more powerful fans and detach the internal walls from each other but has also to account for reverse effects of the more energy consumption and radiation hazards respectively. Fig 13 - Temperature contours for different Prandtls = 0.1 = 0.7 To improve the reliability of the above analysis the following works are recommended: 1- Simulating the flow using the three dimensional geometry. 2- Considering of ventilation from an overhead location in thee dimensional model 3- Considering the effects of variable Prandtl number in solution domain. References [1] Rhie C.M. and Chow W.L., (1983), Numerical Study of Turbulent Flow Past an Airfoil with Trailing Edge Separation, AIAA Journal, 21(11): [2] Versteeg, H., K., Malalasekera, W., H.G., (1995), An Introduction to Computational Fluid Dynamics, Longman Group. [3] Ghia, U., Ghia, K., N., Shin, C., T., (1982), High- Reynolds Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method, J., Comput. Phys., 48(3):