A LOCAL ADAPTIVE GRID REFINEMENT FOR GAS RELEASE MODELING. S.V. Zhubrin. April, 2005

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1 A LOCAL ADAPTIVE GRID REFINEMENT FOR GAS RELEASE MODELING by S.V. Zhubrin April, Introduction The physical and chemical processes responsible for air pollution during the gas releases span a wide range of spatial scales. For example, there may be point sources that are characterized by spatial scales relatively small compared to larger-scale plumes released from such sources. Therefore, to accurately model the transport and chemistry of air pollutants, a gas-release model must be able to adequately resolve the pertinent spatial scales. This can be achieved by local grid refinement i.e. by varying the physical grid node spacing to provide higher resolution where needed. The difficulty with the local grid refinement is that the grid is usually constructed before the details of the solution are actually known; and the transport of species during the gas release often tends to create steep fronts of concentration with large localized concentration gradients. Local adaptive grid refinement provides the technique to overcome this difficulty through the use of grid assignment based upon physical behavior of the flow. The local adaptive grid refinement was applied here to two gas-release problems, namely, hydrogen release within a hallway, and helium release within a garage with a car. In these applications, it will be shown that the solutions with local adaptive grid refinement are more accurate, than fixed grid solutions. In this report, it is described how technique of the local adaptive grid refinement was developed, and implemented in a gas-release model using PHOENICS CFD package. The description details the technique features. The significance of the results is discussed together with further steps required to extend and improve the method. 2 Computational methodology A developed technique of local adaptive grid refinement has two main steps: an adaptation mapping step, which is responsible of finding the regions within the solution domain for the local grid refinement, and refined solution step, that simulates the gas release on the locally refined grid.

2 The solution (i.e. concentration fields) remains unchanged during the adaptation mapping step, and binary adaptation map is generated which marks the regions where finer resolution grids are required. In preparation for the solution step, the adaptation map is used to construct locally refined grid(s) by using embedded (nested) Cartesian grids (adaptive FGEM), or by straightforward increase of regional fineness of the grid nodes (adaptive refined grid), or by combination of two, as appropriate. Ideally, the adaptation mapping should be repeated after each refined solution step owing to the change in the solution fields until the resolution requirements are met. However, for the cases considered here it has proved to be unnecessary; for even first adaptation mapping was usually representative enough for the number of consecutive refined solution steps. The rest of this section consists of a more detailed description of the adaptation mapping and refined solution steps. 2.1 Adaptation mapping step The key to adaptation is an adaptation criterion that determines which grid cell needs to be refined for a more accurate solution. The concentration of the released gas, C, has been selected as an adaptation criterion to detect the existence and track the evaluation of the solution fields on cell-by-cell basis. The Adaptation Marker Allocation Procedure, AMAP, is used to construct the binary adaptation map as follows: 1. The maximum number of absolute values of concentration differences in each cell of calculation plane is calculated as [1]: XY plane: YZ plane: XZ plane: where W, E, S, N, L, H refer to the west, east, south, north, low and high neighbours of cell P. 2. The maximum number of concentration differences in each cell of the solution domain is calculated as 3. The average and standard deviation values of adaptation parameters are calculated as:

3 4. The threshold level for detection parameter is calculated as: 5. If the adaptation parameter of a cell is larger than, then adaptation marker is set to 1.0, otherwise adaptation marker is left as 0.0. The typical adaptation map is illustrated on Fig. 1 Fig. 1 Hydrogen release in a hallway: the adaptation map on an initial coarse grid at a center plane: red marks the cells where Rd is larger than 1.

4 2.2 Refined solution step In preparation for the refined solution step, the adaptation map is used to construct locally refined grid(s), as illustrated further below. The problem of the gas release dispersion is then solved on locally refined grid as described elsewhere. 2.3 Computational algorithm Let it be assumed that the initial coarse grid is constructed uniformly following the distribution of the main objects in the solution domain. The modeling with the adaptive grid refinement proceeds as follows: 1. Solve the transport equations on an initial grid. 2. Based on the concentration field, compute adaptation and detection parameters. 3. Analyse each cell and assemble the adaptation map. 4. Refined the grid locally guided by the adaptation map. 5. Repeat steps 1-4 until the resolution requirements are met. 3 The effects of adaptive refinement on the simulations of gas releases Two cases are considered to evaluate the effects of local adaptive grid refinement on the accuracy of simulations for gas release scenarios. Only steady state cases were considered in this study with PHOENICS of 14 December 2004 being used as a solver. 3.1 Hydrogen release within a hallway. Figure 1 shows the adaptation map produced by the solution of gas release scenario on initial coarse grid The latter is also shown on the picture. The cells which required the grid refinement are shown in red. Figure 2 shows the three-dimensional nature of the adaptation map coloured in blue.

5 Fig. 2 Hydrogen release in a hallway: 3D view on adaptation map. The simulations have been performed using two different turbulence models, namely, standard LVEL and KEMMK with buoyancy correction factor of 0.995, i.e KEMMK In addition to the coarse grid, the performance of KEMMK-0995 model has been tested on three more locally refined grids using both standard repositioning (adaptive refined) and nested, fine grid embedding (FGEM). The both types of refinement have been done in a way consistent with adaptation map. Figure 3 and Figure 4 show the grid distributions at the centre plane and at the solution domain faces, accordingly.

6 Fig. 3 Hydrogen release in a hallway: FGEM-1 - embedded locally refined adapted grid. Fig.4 Hydrogen release in a hallway: FGEM-1-3D view. The adaptive refined grid of 36x20x23 has been obtained by applying the adaptive procedure once, while the two grid levels of FGEM-1 and FGEM-2 are the results of applying the procedure twice. The inspection of Table 1 confirms that the local adaptive grid refinement does improve the accuracy of the simulations, both quantitatively and qualitatively. In fact, the simulation on the

7 initial coarse grid of fails to predict the increase of concentration at the position of Sensor-4 relative to the Sensor-1. This flow feature, however, is realistically captured on adapted grids of all three levels. The accuracy of the predictions at Sensor-2 and Sensor-3 locations does not improve as a result of grid adaptation the fact which can be now attributed to the deficiency of turbulence modelling with more certainty than ever before. It is interesting to see, that the results of standard, but adaptive, local refinement (Adaptive refined) are not very far from the results obtained on much finer (and very time consuming) embedded grids. Table 1. Steady state results for Hydrogen release within a hallway (KEMMK turbulence) Simulations Sensor -1 Sensor-2 Sensor-3 Sensor-4 Experimental observations 1.35% 4.90% 4.95% 1.80% Initial coarse grid, % 5.58% 5.67% 1.42% Adaptive refined, % 5.68% 5.77% 1.70% Adaptive FGEM-1, % 5.73% 5.79% 1.80% Adaptive FGEM-2, % 5.74% 5.72% 1.75% Figure 5 shows the velocity vectors at the center plane predicted on FGEM-1 grid. The corresponding contours of hydrogen volume fractions are shown in Figs. 6 and 7. The much higher dispersiveness of coarse grid simulations is clearly evident.

8 Fig.5 Hydrogen release in a hallway: velocity distribution on FGEM-1 adapted grid. Fig.6 Hydrogen release in a hallway: volume fraction of H2 on initial coarse, , grid.

9 Fig.7 Hydrogen release in a hallway: volume fraction of H2 on FGEM-1 adapted, , grid. In the case of LVEL modelling, the effects of two adaptively refined grids have been investigated, and the results of the hydrogen volume fractions at four sensor locations are presented in Table 2. The local grid refinements have been made conventionally by placing more grid cells in the regions indicated on adaptation map rather than using nested, fine grid embedding. The latter has been found incompatible with LVEL model of turbulence, as implemented in PHOENICS Table 2. Steady state results for Hydrogen release within a hallway (LVEL turbulence) Simulations Sensor -1 Sensor-2 Sensor-3 Sensor-4 Experimental observations 1.35% 4.90% 4.95% 1.80% Initial coarse grid, % 5.57% 5.71% 1.36% Adaptive refined, % 5.79% 5.83% 1.12% Adaptive refined, % 5.81% 5.84% 0.74% The inspection of Table 2 shows that LVEL modelling fails to meet the reality satisfactorily the predictions on adapted grids are in more disagreement with observations than coarse-grid calculations. It is a bit disappointing, but understandable; for the turbulence model makes no provision for interaction between buoyancy and turbulence generation. The latter has proved to be an important effect in the uncluttered space, as the results of using KEMMK-0995 above clearly show.

10 3.2 Helium release within a garage with a car. The release of helium in a walled garage space obstructed by the car represents the flow situation that the LVEL model of turbulence was invented for. So, one would expect it to perform more satisfactorily than for previous case. The simulation results using LVEL on three levels of the grid are presented in Table 3. The adaptation procedure has been applied twice to get locally refined grids starting from the coarse one. The conventional refinement has been used with more grid cells placed underneath of the car and in front of the bonnet as adaptation maps indicated. It is seen that adaptive refinement does indeed helps to reduce the predicted concentrations at Sensor-1 and Sensor-4 locations significantly. The predicted results are now more in accord with the CFD simulations reported elsewhere. The experimental results are unavailable for comparative purposes. Table 3. Steady state results for Helium release within a garage with a car (LVEL turbulence) Simulations Sensor -1 Sensor-2 Sensor-3 Sensor-4 Swain s CFD 0.5% 2.55% 2.55% 1.0% Initial coarse grid, % 2.53% 2.52% 1.94% Adaptive refined, % 2.66% 2.62% 1.08% Adaptive refined, % 2.70% 2.67% 1.01% 4 Conclusions The practical procedure for local adaptive grid refinement has been developed and successfully applied for two typical scenarios of gas releases. It has been shown to be an effective method for improving the accuracy of the predictions. The main advantage of the method and procedure developed is that it allows reliable and computationally inexpensive guidance to be obtained with regard to the specific regions of the flow requiring grid refinement. It is maintained that the adaptation technique developed for this research is sufficiently detailed for general engineering purposes. The AMAP method allowed an adaptation concept to be developed, implemented and applied in a timely manner without re-writing the CFD source code. However, there is a substantial scope for further method development and improvement. The directional computations of adaptation parameters should be provided, in place of simple lumped non-directional analysis. It will allow getting the guidance for the directional grid refinement. The automated adaptive refinement of temporal gridding could also be made along the lines developed above.

11 5 References 1. Shirani E. and Ameri M. (2000) "Effects of directional subdividing on adaptive grid embedding", Report IC/2000/81, UNESCO and International Center for Theoretical Physics, Trieste, Italy