Computational fluid dynamic (CFD). The CFD method is an important method to determine the flow characters of submerged jets into cavities.

Background

With the development of computer resources, the computational fluid dynamic (CFD) has become an important method to analyse fluid dynamic problems, which include aeronautics, automotives, wind turbines and so on. The CFD method is used in a wide range because it could apply overall analysis result in a short time. However, the experiments also need to be employed to validate the CFD results. The flow of submerged jets into cavities is a common problem in fluid dynamic field. It can be found frequently in technical applications, which include engine cooling system, continuously feeded reactors and so on. The CFD method is an important method to determine the flow characters of submerged jets into cavities.

Introduction

The flows of submerged jets in cavities are found in numerous technical applications. With increase of flow velocity, the flow will transfer to high Reynolds number flows. These high Reynolds number flows often exhibit a long-term oscillation behavior of large coherent structures. So that, the determination of characters of flows of submerged jets in cavities is important. The CFD method is employed to analyse the flow characters. However, in the CFD process, the mesh conditions and physics conditions is an important setting. It is because those large eddy simulations would be very time and memory-consuming. Also, in order to simulate both laminar and turbulence conditions, the flow characters of these two flows have been discussed.

Laminar and Turbulent flow

There are two major types of flows, laminar flow and turbulent flow. With the increasing of flow velocity, these two types of flows could transfer to each other. The dimensionless Reynolds number is an important parameter in the equation that describes whether flow conditions lead to laminar or turbulent flow. Each type of flow has its own characters. These two types can be divided based on the Reynolds number, laminar flow occurs at low Reynolds numbers, while turbulent flow occurs at high Reynolds numbers. Based on the value of Reynolds numbers, the types of flows can be divided as below.

Laminar flow generally happens when dealing with small pipes and low flow velocities. Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost parts flow the fastest, and the cylinder touching the pipe is not moving at all. In turbulent flow, the vortices happens, eddies and wakes make the flow unpredictable. Turbulent flow happens in general at high flow rates and with larger pipes.

As previous discussion, the Reynolds number is used to divide flow types. So that, the equations used to calculate Reynolds number need to be introduced. There are different simulations are used to define Reynolds number. In current state, the problem is about flow in pipes, so that the Reynolds number can be defined as below,

Where,

V is the mean fluid velocity.

is the density of the fluid.

is the dynamic viscosity of the fluid.

is the kinematic viscosity.

is the hydraulic diameter of the pipe.

Simulation Processes

In order to achieve accuracy results, the real conditions need to be discussed and simulated. The dimensions of the flow geometry are shown as Fig.1. Because the model is fed by water circuit, so that the flow properties, density and kinematic viscosity can be determined, which are and . Also, as definition, the diameter of pipe is , which is also the hydraulic diameter of the pipe. The purpose of this course work is to simulate flows in laminar and turbulent conditions, so that the input velocities need to be calculated in both conditions. In order to calculate the velocities, the Reynolds numbers in laminar and turbulent conditions are assumed. Based equation 1.1, the velocity in specific Reynolds number can be expressed as equation 1.2.

In the current problem, the Reynolds number of laminar flow and turbulent flow are assumed as 1500 and 6000 respectively. With assumed Reynolds number, submit them into equation 1.2, the input velocity for simulation can be calculated as 0.0556m/s and 0.2222m/s for laminar flow and turbulent flow. Because the flow is in a tank, so that the reference pressure of simulate is set to 0 Pa, the pressure at outlet is atmosphere pressure, which is about 100000 Pa.

Fig.1. Dimensions of the cavity given in mm

The model of cavity is created in CATIA, and then input to STAR-CCM+ in stl.file. The model is modified in STAR-CCM+ to different boundaries which have different boundary conditions. In this simulation, there are three types of boundary are used, which are velocity inlet, pressure outlet and wall. The boundary setting can be seen as Fig.2.

Fig.2. The boundary conditions of geometry

After modified geometry, the next step is set the mesh conditions and physics conditions under continua menu. In mesh condition setting, the following models have been ...

This is a preview of the whole essay

Fig.1. Dimensions of the cavity given in mm

Fig.2. The boundary conditions of geometry

After modified geometry, the next step is set the mesh conditions and physics conditions under continua menu. In mesh condition setting, the following models have been chosen, which is shown in Fig.3.

Fig.3. The mesh conditions of the simulation.

Polyhedral mesher provides a balanced solution for complex mesh generation problems. They are relatively easy and efficient to build, requiring no more surface preparation than equivalent tetrahedral mesh. The polyhedral meshing model utilizes an arbitrary polyhedral cell shape in order to build the core mesh.

Surface wrapper is used to provide a closed, manifold, non-intersecting surface when starting from poor quality CAD data. It is typically used when the imported surface includes problems, such as multiple, intersecting parts; missing data in the form of holes and gaps; surface mismatches; double and internal surfaces and over complex geometry with too much detail.

Surface remesher is typically used for remeshing surfaces produced by the surface wrapper. As well as improving the surface for the volume meshers it also aids the subsurface generator when the prism mesher option is selected.

After choosing the mesh models, the following reference values need to be setting, which are base size and surface curvature. The base size value is a characteristic dimension of the model that should set to using any relative value parameters in reference values node. The value can be set in any of the normal length units. The smaller of base size setting, the model will be divided into more cells. Surface curvature node allows cell refinement to be included for the surface wrapper, surface remesher and trimmer mesh models based on the number of points around a circle.

Fig.4. The reference values setting of mesh conditions.

After mesh models have been set up, the volume mesh needs to be generated. The Fig.5 shows the mesh conditions.

Isoview of the solution domain (b) shroud and parts of the cavity lid

Fig.5. Numerical grid for the simulations.

After set up the mesh conditions, the physics conditions need to be set up. The following physics models have been chosen as shown in Fig.5. There are two different physics models have been chosen for laminar and turbulent respectively.

a b

Fig.6. Physics models of simulation. (a. physics models for laminar simulation. B. physics models for turbulent simulation.)

The boundary conditions are steady-state conditions even in the unsteady simulations [1]. And all simulations are performed with segregated solve [1], so that the segregated flow has been chosen. The flow in the current state is water flow, and then the liquid setting has been chosen. In real condition, the water density will not be changed or slightly changed, so that it is set Constant Density. The laminar and turbulent are chosen for different conditions. In turbulent setting, the K-epsilon turbulence has been chosen.

The last step is running simulation. In order to achieve accuracy results, the simulation must converge. The residuals plot is used to monitor converge of simulation. The simulation converges when all properties lines become steady, which is shown in Fig.7.

Fig.7. Simulation converge monitor plot.

Make sure the simulation is converged. The plots of velocity and pressure are needed to be used for comparison. There are five planes have been created to plot overall performance of results, the planes are shown in Fig.8.

Fig.8. The five planes for data plot.

Mesh Comparisons of Laminar flow

The mesh models have been chosen and introduced in last section. There are two reference values need to be set, base size and surface curvature. The surface curvature is used to optimize the mesh, so that it will not be changed in mesh comparison. The different base sizes have been set and simulated to analyse the affection of mesh size. The mesh comparison is under laminar conditions with different base size, which are 10mm, 12mm and 20mm respectively. The different base sizes create different cells of simulate, the smaller base size will create more cell of simulation. This will increase the accuracy of results. However, with increasing of cells, the simulation time will also be increased. So that different base sizes are tested and the results are compared. The base size, which can perform acceptable results with less simulation time will be chosen, and used in simulation of turbulent flow. The simulation results of different mesh sizes for laminar flow are shown as figure.

In left figure, it shows the overall performance of different base mesh size. In the simulation process of 10mm base mesh size, it takes about 6 hours to make the simulation converge. And for rest two simulations, it just takes about 3 hours to make simulation converge. From the table 1, the cell number and results are compared; it could be found the results of these three simulations are slightly different. Also, in current study, there are not high quality requirement of results. So that base size 12mm will be chosen for turbulent simulation, this could achieve acceptable results and significantly reduce the simulation time.

Table.1. Results comparison of different base mesh sizes

Comparison of laminar flow and turbulent flow

Fig.9. Physics values setting of turbulent flow.

As discussed before, the physics conditions of laminar and turbulent flows are different. Also, as an important property, the turbulence intensity needs to be modified. It is set to 5% in this problem [1]. The base mesh size is chosen as 12mm. The turbulent flow performance will compared with laminar flow performance.

Fig.10. Velocity vector plots of laminar flow in plane 1 and 5

Fig.11. Velocity vector plots of turbulent flow in plane 1 and 5.

From Fig.10 and Fig 11, the flow characters of laminar and turbulent can be seen. In Fig.10 the laminar flow is steady. The flow moves to same direction. However, in the Fig.11 the turbulent flow is unsteady. The vector plot of turbulent is much massive than laminar. There are vertex happens in turbulent condition.

In order to show completely performance of laminar and turbulent flow, the streamline of flows are plotted, and they are shown in Fig.12.

a b

Fig.12. The streamline plots of laminar and turbulent flow. (a. Laminar flow. b. Turbulent flow.)

In Fig.12, the flows performance from inlet till outlet can be seen. The part a is stream line plot of laminar flow. It can be seen from plot, the flow velocity is accelerated in pipe section. Then the flow is divided into two vertex sections, one is flow A, which is clockwise rotate at front of inlet section; the other is flow B, which is rotating and moving to outlet section. The flow A and flow B mix at middle section of tank, then move together through outlet. Because the velocity of flow A and B is slow, the mixture of these two flow does not cause unsteady condition, and there are not many vertex happen. The mixed flow steady enter outlet pipe and the velocity of flow is slightly accelerated. In part b of Fig.12, it can be seen the turbulent flow also divided into two flows after through inlet pipe and the flows are named as flow C and D. However, there are not too many flow line at the front section of tank, this means the flow C moves fast and flow does not steady long. The flow C and D mix much faster than flow A and B. Because of high velocity of flow C and D, when mixture happens, it causes lot of vortex and the mixed flow become unsteady. The unsteady flow continues until flow through outlet pipe.

In this section, the flows performances of laminar and turbulent have been plotted. The characters of these two flows can be clearly seen. The velocity of laminar flow is much slower than turbulent flow, and it leads flow to steady condition. In turbulent flow, because of massive and high speed, there are many vortex happens in all sections.

Comparison results with previous CFD simulation

The CFD method is employed to analyse the problem, and the results have been got. However, without experiment validate, the results need to be compared with previous work. Relative to the research of R.Schwarze, the turbulent flow conditions are compared. The turbulent model is chosen as standard. The vector plot and velocity distribution along the section are used for comparison.

Fig.13. The CFD plots of plane 1 and 4

Fig.14. The plot from previous simulation.

From the vertical section vector plots, it can be seen the flow performances are similar. These two plots show the same flow condition, which present two vortexes in this section. The left vortex rotate clockwise and the right vortex rotate unit-clockwise. The right vortex is much stronger than left one. In the horizontal section vector plots, the performances of flows are also similar. However, from the CFD plot, the vectors are not clear, it is because Star-ccm+ make the vector length proportion to velocity value. At end section of tank, the velocity is significantly low, this lead the vector short and cannot be clearly shown. But the overall performance are similar, this means our works are matched with previous work. After compared vector plot, the velocities plot along the line will be compared. A line is created in the middle section of geometry; the velocity along the line is plotted and compared.

Fig.15. Creation of velocity plot line.

And the velocity along the section and be plotted as Fig.16

Fig.16. Velocity distribution along the line and plane section 5

Fig.17. Velocity distribution along the middle section for previous work.

Because of reverse direction of geometry, the coordinate system of plot is different. The Fig.16 needs to be read from right hand side to left hand side. The input velocities are different, so that the trends of plots are used for comparison. It can be seen trends of these two plots are similar, which goes up at beginning, then decreases, finally becomes steady. This means our work matches with previous work.

Discussion

As an important method, the process of computational fluid dynamic (CFD) method has been employed to analyse turbulent round jet into a cavity. In the simulation process, there are two important settings need to be done, mesh models and physics models. The correct mesh models will affect the mesh quality of geometry. Even more, with selecting correct mesh models, the poor import geometry could be optimised. In mesh process, the geometry is divided into amount of cells. These cells are used in further analysis process. The more cells divided, the more accuracy results will be achieved. However, with more cells, the simulation time will be significantly increased. The ideal condition of mesh size is achieving acceptable accuracy results with shortest simulation time. The different mesh sizes have been compared in laminar condition, there are three different base sizes have been chosen, which are 10mm, 12mm and 20mm. It can be found the results of 10mm and 12mm base mesh size are much different from 20mm base mesh size. This means the 20mm base mesh size is not accuracy enough. Comparing 10mm and 12mm base mesh size, the results are slightly different, but simulation time of 12mm base mesh size model is significantly reduced. So that, it can be concluded that the 12mm mesh size is optimal mesh setting in these three base sizes. As another important factor, the correct physics models need to be selected. The selection of physics models should based on real condition with Navier-Stokes equations. The different physics models are designed for different conditions, such as flow is compressible or not. The simulation condition needs to be modified based on specific problem.

There are two major flow types, laminar and turbulent flow. These two different flows are distinguished from their own flow characters. The laminar flow is slow, steady and no disruption between the layers. The turbulent flow is unsteady and rapid variation of pressure and velocity in space and time. In CFD simulation, the performances of these two flows have been analysed and velocity vectors have been plotted. The characters of laminar and turbulent flows can be clearly compared. The turbulent flow is much massive than laminar flow, and there are lots of vortex in turbulent flow. The CFD results are compared with previous work. The results are slightly different from previous work. The computer sources might be a reason for this. Because of computer sources limitation, the geometry mesh cells are limited, the accuracy of results are affected. The software used for simulation are different too. The simulation equations might be slightly different. This might be another reason causes the errors.

The experiment method is important and used to validate the CFD results. The real conditions are performed in experiment. However, there must have different between experiment and CFD analysis. It is because the CFD method simulates the ideal condition, even it is well modified, there are still some factors have not been considered. As another aspect, the CFD method is used to apply general performance. It will need huge computer source to simulate all factors. This will waste lots of time and money.

Conclusion

In conclusion, the computational fluid dynamic (CFD) method to analyse flow characters has been learnt. As an important factor of CFD simulation, the mesh size needs to be modified. The purpose of choosing mesh size is to achieve acceptable accuracy results and reduce the simulation time. The modification of simulation process is introduced, which is important to accuracy simulation results. In order to achieve accurate results, the simulation must converge. With the CFD results, the characters of laminar flow and turbulent flow are compared and known. The Reynolds numbers are used to determine flow is laminar or turbulent. The formulas of calculating Reynolds number are learnt. The CFD simulation results of turbulent flow are compared with experiment results. The experiment method is an important to validate CFD simulations.

Reference

Rudiger Scharze, Jens Klostermann, Christoph Brucker, Experimental and numerical investigations of a turbulent round jet into a cavity. Inernational Journal of Heat and Fluid Flow2008
H. Fellouah, C.G.Ball, A.Pollard, Reynolds number effects within the development region of a turbulent round free jet. International Journal of Heat and Mass Transfer, Volume 52, Issuse 17-18, August 2009. Page 3943-3954.
Janyalertadun, Computational fluid dynamic modeling of an inlet in a cross-flow, 2000.