Numerical Investigation of Single Phase Flow Oscillatory Baffled Columns - Coursework Example

Numerical Investigation of Single Phase Flow Oscillatory Baffled Columns Roger J 1Institute of ?????, of ????? Flow development in oscillatory baffled columns (OBCs) has been investigated at length in laboratory conditions but the application of numerical techniques has remained limited. The development of flow inside OBCs has been investigated through numerical methods in order to discover the most suitable models for modelling such flows. Numerical results have been compared to previous laboratory experiments from other researchers in order to ascertain the suitability of the utilised models. Results demonstrated that the inclusion of eddies in OBC flows requires the use of LES-WALE turbulence model to achieve reliable results. 1 Introduction OBCs have been under investigation for some time now given the advantages they provide compared to conventional mixing and reaction vessels. The greatest amount of research concerning flow characterisation inside OBCs has been performed in laboratory conditions only. Though carrying out laboratory experiments is required for scientific validation but this process could be simplified through the use of computer aided means. Advances in numerical modelling and solution techniques over the years have meant that computer aided simulations can be used just as reliably as laboratory experiments in order to investigate physical phenomenon. However, in order to utilise computer aided means, it is necessary to find fitting solution models for the situation provided since there is no one size fits all solution methodology through numerical solutions. The current research has undertaken the discovery of fitting models that are required to simulate and find solutions for flow inside OBCs. In order to carry out this research, the researcher has utilised ANSYS 13.0 in collaboration with CFD software. All simulations carried out in order to further this research were based on single phase flows only. In addition, three different scenarios were investigated where the diameter, the frequency and the amplitude were varied respectively. The results from these computer simulations were compared to previous laboratory research from published and validated researches. The contention was to apply various different computing models in order to decipher which models were best suited to OBC flow phenomenon. In addition, the primary area of investigation remained flow turbulence emulation since turbulence plays a vital part in mixing inside OBCs. Three different turbulence models were used namely LES, DES and k epsilon. 2 Single Phase Flow Investigation The study was conducted to investigate the response of flow in OBCs as various parameters were modified. Three sets of geometry were used to carry out the investigation that was comparable to previous literature in use. The diameter was varied between 50 mm, 100 mm and 200 mm to carry out the investigation. Another investigation was also carried out using variations in the frequency and amplitude to decipher their effects on the flow characteristics. The diameter for the frequency and amplitude study was restricted to 145 mm for it to be comparable to previous literature on the issue. 2.1 General Parameters 2.1.1 Numerical Set Up The model used for simulation consists of two orifice baffles that tend to form three different baffled cells. The cell of interest is the middle cell as the bottom and top baffled cells do not replicate baffled flow. The working fluid for this simulation is water at room temperature possessing a density of 998.2 kg/m3 and a viscosity of 0.001003 kgm/s. Three different models were used to deal with the turbulence namely LES (Large Eddy Simulation), k- and Detached Eddy Simulation (DES) model. The diameter variation study as well as the amplitude and frequency variation studies used these parameters. 2.1.2 Geometry Figure 1 - Geometry and Boundary Conditions Setup for diameter variation study (left) and amplitude and frequency variation studies (right). The geometry for the simulation is represented above and was kept constant throughout the entire study. The basic ratio between L and D was kept constant at 1.5 while the baffle thickness was also fixed at 3 mm irrespective of any other parameters. In addition the square of ratio of orifice diameter to total diameter was maintained strictly at 0.22 in order to promote mixing consistency. The diameter variation study utilised three sets of geometry including D = 50, 100 and 200 mm. In contrast, the amplitude and frequency variation study was carried out using one fixed diameter which was 145 mm. 2.1.3 Boundary Conditions Diameter Variation Study The primary boundary conditions used for this study were implemented at the inlet, the outlet and the walls. The inlet was supplied with a periodic mass flow rate as opposed to periodic velocity that has been utilised by other studies on the matter. The mass flow rate implemented at the inlet was of the form: In contrast the outlet was provided with an opening type boundary condition with a relative pressure of 0 Pa providing it similar mass flow type characteristics though both are not exactly the same. Moreover the walls for the study were provided the default non-slip wall type boundary condition. Frequency and Amplitude Variation Study The primary boundary conditions used for this study were implemented at the inlet, the outlet and the walls. The inlet was supplied with a periodic inlet velocity as opposed to periodic mass flow rates that was utilised for the previous investigation. The periodic velocity implemented at the inlet was of the form: In contrast the outlet was provided with an opening type boundary condition with a relative pressure of 101325 Pa. Moreover the walls for the study were provided the default non-slip wall type boundary condition. 2.1.4 Mesh Set Up The mesh was created using the default ANSYS Workbench 13.0 mesher using size controls. The smallest size of the mesh was kept at 3 mm in order to deal with the baffle thickness appropriately. All meshes for this study relied on this principle while all other settings were kept at default. Figure 2 - Mesh Setup for Diameter Variation Study 2.2 Diameter Variation Study 2.2.1 Operating Parameters The final set of operating parameters achieved for the purposes of this study are summarised in the table below: Diameter (mm) 50 100 200 (mm) 4 5 6.4 St 0.995 1.592 2.487 f (Hz) 1 1 1 (mm/s) 4 5 6.4 (mm/s) 25.1 31.4 40.2 1257 3142 8043 Ratio of - 2.5 2.56 2.2.2 Results Figure 3 - Surface (y = 0) and cycle averaged mean velocity versus column diameter from (Jian and Ni, 2005) Figure 4 - Surface (y = 0) and cycle averaged mean velocity versus column diameter for the current study The results from Jian and Ni (2005) were used as a benchmark to conduct this study. The original study investigated the variation in surface and cycle averaged mean velocity against the column diameter for three diameters that were 50, 100 and 200 mm. The current study replicated all boundary conditions and other stipulations and investigated flow using three different turbulence models namely LES (Large Eddy Simulation), k- and DES. In contrast, the original study used a simple laminar and turbulent switch model for dealing with the turbulence. Based on the results presented above it is clear that the LES model is best able to replicate the results of the original investigation. The k- model tends to underestimate the overall velocity by a fairly large amount providing an overall variation of 20% on all three points. On the other hand, the DES model tends to overestimate the velocities but the variation is lower than that for the k- model although the direction of variation is altogether different. The deviation in the DES model is not constant but tends to increase as the diameter is increased keeping all other conditions constant. The variation in velocity can be seen to vary from some 5 to 10% from the first run to the last run. Based on these findings it is clear that the LES model tends to replicate the findings of the original study far more accurately than the other models. Based on the results of this simulation it is clear that the mean velocity tends to decrease as the diameter of the baffled column is increased. The decrease in velocity can be seen as directly related to the increase in the column diameter. The mean velocity for a baffled column with a 50 mm diameter was 0.06 m/s which decreased to 0.51 m/s for a 100 mm diameter column which further decreased to 0.48 m/s for a column with a diameter of 200 mm. It can be seen from these results that the decrease in mean velocity also tends to decrease as the column diameter increases. Hence, when a column is being scaled up, there will be ostensible decreases in the mean velocity which lends credence to the belief that the mixing will suffer as well if it were already optimised for a smaller column. This has large implications for the scale up behaviour of baffled columns because when baffled columns are being scaled up there will be need to bolster parameters such as the frequency and amplitude in order to obtain similar mixing characteristics. Velocity Vector Maps from Jian and Ni (2005) Velocity Vector Maps from the Current Study, Phase Four D = 50 mm D = 100 mm D = 200 mm 2.3 Frequency and Amplitude Variation Study 2.3.1 Operating Parameters This part of the investigation can be seen as a continuation of the previous study as similar geometry was used with some differences in the boundary conditions. The table below depicts the final set of operating parameters along with operating parameters from the previous study (highlighted). Diameter (mm) 50 100 145 200 (mm) 4 5 5.7 6.4 St 0.995 1.592 2.024 2.487 f (Hz) 1 1 1 1 (mm/s) 4 5 5.7 6.4 (mm/s) 25.1 31.4 35.8 40.2 1257 3142 5168 8043 2.3.2 Results The mixing present within the column needs to be classified on the basis of some kind of numerical parameter(s) that would help determine the amount and extent of mixing present. In order to deal with this the parameter of choice was the ratio between the surface averaged axial velocity and the surface averaged radial velocity. Mathematically this can be expressed as: The results of the subject simulations reported that should be kept between 2 and 2.5 for OBCs to ensure optimal mixing. Given the conditions of the numerical simulation such as the boundary conditions, the fluid domain and the turbulence control it was found out that the ratio tended to vary between various models being used for turbulence modeling. The k- turbulence model showed the greatest variation with certain values for instantaneous velocity ratio ranging in the thousands. This was attributable to the massive decreases in the radial velocity that the k- model was unable to cater for. The dismally low radial velocities biased the velocity ratio to very high values though this was temporal. The overall average for velocity ratio obtained using the k- model was the highest ranging to as high as nearly 10. In contrast, both the LES and the DES model were able to offer better estimates for velocity ratio. The velocity ratios achieved using the LES and the DES model remained around 2.5 which is seen as an optimal ratio to achieve optimal mixing in baffled columns. The turbulence model based variations were apparent for both changes in the amplitude and the frequency. 2.4 Effect of Amplitude Variation Figure 5 - Variation of velocity ratio with amplitude from (K. S. Wah et. al, 2012) Figure 6 - Variation of velocity ratio with amplitude for the current study The graph presented above clearly depicts that the LES and the DES turbulence models are able to replicate flow conditions inside a baffled column. However, the results displayed by the k- model demonstrate that it is not reliable enough to decipher the flow conditions in baffled columns. Additionally, the variation through the k- model is too large to be ignored in terms of the velocity ratio. These large variations are largely present due to turbulent mixing that produces dismally low radial velocities in the k- model leading to very high velocity ratios. For example, the variation at amplitude of 5.5 mm is around 19.34 times (velocity ratio of 9.65 for the k- model and 0.55 for the LES model). Similarly the other amplitudes under investigation show little resemblance to the original plot for the k- model leading to the belief that it is unreliable to model turbulent flows inside baffled columns. On another note, the velocity values achieved through the use of the LES and the DES model tend to vary amongst themselves as well. The LES model velocity figures are slightly higher than those for the DES model values which is understandable given the large dissipation involved in the DES model. Even so the actual variation between the LES model and the DES model is between 6 and 24%. The slightest of these variations is at amplitude of 5.7 mm while the greatest variation is at amplitude of 5.9 mm. All other variations in amplitude between the LES and the DES model are around 10% in magnitude which indicates that either model could be used for investigating flows in baffled columns. 2.5 Effect of Frequency Variation Figure 7 - Variation of velocity ratio with frequency from (K. S. Wah et. al, 2012) Figure 8 - Variation of velocity ratio with frequency for the current study When the effects of frequency variation are seen between different turbulence models, it becomes clear that the LES model tends to replicate the results of previous studies such as the results by K. S. Wah et al. (2012) Much like the amplitude variation investigation, it is clear here too that the k- model is not able to deliver in this situation again largely due to the presence of turbulence. The k- model tends to provide velocity ratios that are initially too high and then too low to support previous results. In contrast to this, the DES model tends to follow the original results well enough for outliers such as frequency of 0.4 Hz and 0.6 Hz but fails to account for the nuances between frequency of 0.5 and 0.55 Hz. This could be attributed to variations in velocity especially radial velocity due to excessive dissipation effects. In contrast, the LES model is able to model the situation with far greater ease. Throughout both the investigation on amplitude and frequency, it has become clear that the LES model is able to predict actual flows inside baffled columns in the turbulent regions. However, it must be borne in mind that there were slight variations in magnitude between the LES model and the results of previous studies that remained under 10%. This could be attributed to the use of more nodes for this study, the use of 3D investigation against 2D investigation and differences in solvers and error control. Upward Stroke Downward Stroke 40.1 s 40.3 s 40.5 s 40.6 s 40.8 s 41.0 s 40th cycle =1.0 Hz = 5.7 mm Figure 9 - Comparison of Velocity Contour Maps from the Current Study and Wah et. al (2012) 2.6 Inferences The current numerical simulations were able to replicate most aspects of the study under discussion. The major phenomenon at hand was significantly similar though variations in timing and phase cycles were a constant feature of the produced results. However the surface average mean velocity remained the same for all involved cycles which in turn leads to the belief that the aberrations were produced by instantaneous changes in radial velocity. As mentioned previously optimal mixing requires a certain degree of turbulence (as is high and between 2 and 2.5) so it is pertinent to pursue a 3D numerical study using a holistic geometrical approach to analyze the mixing in greater detail. This approach tends to consume greater time (roughly 12 to 15 hours for each simulation) but tends to produce results that stand in agreement with previous experimental results and literature. Since single phase flow has been investigated in detail beforehand as well (evidenced by the large amount of literature on the matter) so a new approach was created in order to investigate two phase flow. 3 Contribution of Current Research The application of numerical solutions to OBC flow patterns through the use of computing platforms has remained limited. There has been scant research on the use of computing platforms to deal with OBC flow patterns and their characteristics. It has been more common to use scaled up laboratory experiments in order to study the various characteristics of OBC flow patterns. This has remained true for both single phase and two phase flows developed inside OBCs (Oliviera, 2004). In other cases when numerical solutions for OBC flow patterns are developed, the research is often limited on a number of different accounts. For one thing, the methods utilised in order to solicit numerical solutions are often not fully described. It is often difficult to comprehend what form of computing platform and software have been utilised in order to carry out a certain research regarding OBCs. It is typical to find lengthy literature reviews and descriptions of the requisite investigation area without much thought given to the solution creation mechanism. The use of two typical platforms CFD and FLUENT presents a number of differentiated constraints when working and incomplete solution descriptions make future research all the more challenging and vague. In a similar manner, numerical solutions through computing platforms often lack a decent description of the exact methods being used. Modern computing platforms provide a number of different options to simulate flow patterns that require meticulous matching and fitting in order to solicit the right software model for the situation being investigated. The lack of properly detailed descriptions of software models (such as the turbulence models) being used only leads to discounted credibility for the research being undertaken. Moreover, the essential scientific element of traceability tends to abrade given that current numerical researches on OBCS tend not to include viable descriptions. Another major limitation of current numerical research on OBCs has been the use of limited computational models in order to spare the time and the effort. It has been common to see a progression of numerical research on OBCs where 2D models evolved into 3D sector models. The results produced by numerical simulations utilising 2D models have been greatly simplified and fail to take into account the many radial velocity variations that affect OBC flows especially in the later cycles. The same is true of 3D sector models where certain sector based geometrical arrangements are used for numerical simulation assuming that the flow is symmetrical. However, as the current research has proved that flows inside OBCs are only symmetrical for simplified models as well as for the early phases. Once large radial variations begin to occur, especially in flows where the velocity ratio exceeds 3, the 3D sector approach also fails to account for myriad flow variations. The current research has shown beyond doubt that numerical investigation of flows inside OBCs requires pure 3D models especially for situations where the normal operating parameters are being exceeded. Additionally, the representation of results in the current literature bank has been limited by certain aspects. Certain forms of research have presented their results through visual means, others have relied on graphing velocity and yet others have taken onto the more esoteric power density. The current research has used a number of different output parameters in order to characterise the results such as axial velocity, radial velocity, velocity ratio, power density etc. The contention in using a large number of parameters to report the same results is to allow for greater traceability and reproducibility while also providing for variation in various parameters in the same situation. It is deemed that this would aid future investigation and research into this area as detailed results are available for a number of different situations. Overall, it could be surmised that the existing research in this area, especially numerically investigated results, provide that numerical means can be utilised in order to simulate flows inside OBCs. The current research has taken this position forward to allow for a systematic application of software models and methods in order to simulate flows inside OBCs. 4 References Read More