Computer Simulation Based Optimization of Aspect Ratio for Micro and Nanochannels

For Computational Fluidic Dynamics (CFD) analysis, different types of software are available such as ANSYS, COMSOL, GAMBIT and ABAQUS. ANSYS FLUENT is a very influential CFD software that enables the researchers to execute advanced and fast simulation as the performance of product is optimized. In this research work, the capabilities of ANSYS FLUENT have been investigated through the fluidic simulation of nano scale channels. Here, the simulation of three straight shaped and one curvilinear nano channel has been performed to analyze the precision of simulation with the aspect ratio of smaller dimensions (radius, length). The accurate dimensions have been determined for various shapes of channels. For straight circular channel, the radius of 124.9 μm and length of 900 μm are the dimensions found for error free simulations with 7.20 aspect ratio. While for straight crossed channel, the radius of 5.1 mm and length of 100 mm are the accurate dimensions for error free simulations with 19.60 aspect ratio. Width and depth are determined as 180 μm with 180 μm length in case of straight square channel for error free simulations with 1.0 aspect ratio. Finally, in case of curvilinear channel for error free simulations, the radius and length are found 22 and 209.1 μm respectively with 9.50 aspect ratio. None of the channels is found fit for simulation in nanometer range. Even in micrometer range, the simulations of these channels have acquired errors. Moreover, it has been observed that the aspect ratio is different for different geometries of microchannels for error free simulation.


INTRODUCTION
FD is the use of applied mathematics, physics and computational software to visualize the flow of liquid. CFD analysis presented a complex, fast, effective simulation of transfer of heat, mixing, unsteady and compressible fluid flows [1][2]. Through CFD analysis, the fluid forces can be determined and performance of impact of a liquid or gas can easily be understood. Gas and fluid flow with transfer of heat, internal and external flow of the liquid, turbulent, laminar, and transitional flows, gas and fluid mixing, viscous and non-viscous fluid, real and compressible 780 can be used to innovate with breakthrough capabilities in microfluidic devices such as microchannels, micropumps and microneedles. CFD analysis through ANSYS is used in microchannels research like convective heat transfer, validation of microchannel cooling, heat transfer, pressure loss measurements, flow characteristics and micromixing modelling [8][9]. The overall consequence of aspect ratio on fluid flow in a micro/nano-channel is examined by ANSYS in this paper. Beforehand, the literature has the investigations for the flow parameters on geometrical parameters on micro/nano-channels. But in this study, the authors have simulated micro/nano-channels for better fluid flow. The capability of ANSYS software has been checked extensively. Here, the effect of aspect ratio has been explained by varying the diameter and the length of the channels.
CFD analysis of straight channels cannot be done without the aspect ratio. It is the ratio of maximum dimension to minimum dimension of the channel used. It is a significant factor in flow analysis for microchannels. Rosaguti et al. [10] used ANSYS CFX-10 for sinusoidal microchannels to study heat transfer at low Reynold numbers. They used very low aspect ratio i.e. 4.5 for CFD analysis. Lee et. al. [11] examined the influence of the aspect ratio on rectangular microchannels. Ashraf et. al. [12] used aspect ratio with 160 µm length and 15 µm diameter for cell sorting system through sinusoidal microchannel. Tayyaba et. al. [13] used high aspect ratio with 1600 and 15 µm diameter for cell sorting system through sinusoidal microchannel. Solehati et. al. [14] used high aspect ratio with 10,000 µm length and 500 µm for mixing performance in T-junction sinusoidal microchannel. Ozkan and Erdem [15] used COMSOL Multiphysics software to study the mixing performance in sinusoidal microchannels with aspect ratio of 100 µm length and 0.5 nm diameter. Chiam et. al. [16] used Solidworks and ANSYS with the aspect ratio of 2 for investigation of heat transfer through sinusoidal microchannel. Mixing performance in Tjunction microchannel has been investigated to study the effect of the aspect ratio for flow analysis, fluid velocity and mixer microchannel [17][18][19]. Nivedita et. al. [20] used low aspect ratio for studying the Dean flow dynamics through spiral channels. Damian et. al. [21] examined three crossed microchannels with their aspect ratios. Afzal et. al. [22] [23] have studied the heat flux from microchannels by using high aspect ratio. Previously and presently, all the researchers working on CFD have done the ANSYS simulations on individual element [24][25]. The usage of a computer to characterize the fluid dynamics in micro/nanochannels and in other fields is wide spread [26][27][28][29].

Mesh Dependence
Mesh dependency is used for the following steps for every simulation. For fine mesh analysis, relevance is set at 0. The size function is set at curvature. Fine relevance center is selected. Maximum face size is set at 0.38205e-003. Inflation option is set at smooth transition. First simulation has been run with initial mesh with the confirmation of convergence. Once the convergence criteria were selected for the initial simulation, mesh has been improved globally. Because the solution varies with the modification of mesh, the solution is mesh dependent. Hence mesh dependency was engaged.

ANSYS FLUENT SIMULATION FOR NANOCHANNELS
In this research work, straight circular, straight crossed, straight square and curvilinear nanochannels were investigated extensively through ANSYS FLUENT simulations. From the function of "Create/Edit materials" water was selected as the flowing fluid from the "Fluent Database" in the set up tool of "ANSYS FLUENT". Then boundary conditions were set with 0.1 m/s velocity and 100 Pa pressure. These conditions were kept for all simulations of each and every size of nanochannels.

Straight Circular Nanochannel
First of all, in design modeler micrometer unit was selected because there was no smaller unit available than this. The units available were meter, centimeter, millimeter, micrometer, inch and foot. If a nano size element is to be created in design modeler, then there 781 is a compulsion in ANSYS to opt micrometer as a unit. Because there is no nano unit manufactured in ANSYS, therefore, for nano size 0.001 µm was used as 1 nm. One could use even lower than 1 nm by selecting this scale in ANSYS FLUENT. Although less than 3 nm is not available in some versions of ANSYS. Straight circular nanochannel was designed in design modeler and meshed in mesh analysis. The number of nodes and elements were increased and decreased in mesh analysis by varying the relevance between 0-100 for better mesh. It could also be enhanced by varying minimum size, maximum size and maximum face size of the element used in sizing tool. In sizing tool of mesh analysis relevance center and smoothing were set at fine and high respectively. Also, the function "Use Advanced Size Function" was set on curvature. The geometry of the channel was created in design modeler and meshed in mesh analysis which is shown in Fig. 1. After setting of "Reference Values", "Hybrid Initialization" method was adopted in the "Solution Initialization" tool from setup. During simulations different errors occurred. The errors "Divergence detected in AMG solver: Pressure correction" (accuracy for radius up to 300 nm and length up to 3 µm), "Divergence detected in AMG solver: xmomentum" and before them a warning error "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" occurred when straight circular nanochannel was considered. If pressure and velocity were changed to get rid of the error of "Divergence detected in AMG solver: Pressure correction" then the error of "Divergence detected in AMG solver: x-momentum" occurred and vice versa. These errors could also have occurred in bigger channels when there was wrong shape of geometry, wrong mesh and wrong boundary conditions ( Fig. 2(a-c)). With these errors, there were no simulations. Actually, these are the errors of ANSYS which cannot handle the nano size element. When the dimensions of the channel were increased up to 300 nm radius and 3.1 µm length, with the same boundary conditions then these errors were eliminated automatically and simulation was performed with the same warning error "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" that appeared in setup tool of ANSYS. The contour of pressure for this simulation is shown in Fig. 3.
With the warning error, the received data had first five zero iterations from the total iterations. This type of

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warning could be ignored. Then flow velocity, flow rate and other parameters could be determined easily from the obtained data. The first five zero iterations can be observed in Fig. 4.
When radius was decreased from 300-299.9 nm, a new error "1 solution is converged" occurred. Simulation was not done with this error. When the size was more increased from nano size to 71.1 µm radius and 400.1 µm length then warning error was eliminated with the same boundary conditions and simulation was not done. This time the error was "2 solution converged". At 80 µm radius and 500 µm length, the error "3 solution is converged" occurred. Still no simulation was done. The error "4 solution is converged" occurred at 100 µm radius with 500 µm length. Finally, the error "5 solution is converged" occurred up to 124.8 µm with 900 µm. These errors are shown in Fig. 5(a-e). These errors meant that the fluid could not enter the channel and flow was converged. Fluid could not pass through the channel. When the size was adjusted above or equal to 124.9 µm radius and 900 µm and error free simulation was done at this range. When length was readjusted up to 899.9 µm then again simulation was not done. The contour of pressure for this simulation is shown in Fig. 6. With warning error simulation was done for straight circular microchannel at 103.3 aspect ratio. Error free simulation was done for this microchannel at 7.20 aspect ratio. It means ANSYS works best with these dimensions for straight circular microchannel. The summary of the simulated data is shown in Fig. 7. The errors are along y-axis and dimensions are along xaxis.

Straight Crossed Nanochannel
The name straight crossed was given to this type of nanochannel because of two straight perpendicular nanochannels. This nanochannel was created in nano size and meshed in design modeler and mesh analysis respectively. The number of nodes and elements were varied in mesh analysis by changing the relevance between 0-100 for accurate mesh. It could also have enhanced by varying minimum size, maximum size and maximum face size of the element used in sizing tool. In sizing tool of mesh analysis relevance center and smoothing were set at fine and high respectively. Also, the function "Use Advanced Size Function" was set on curvature. Figu 8 from design modeler and mesh analysis for this nanochannel are shown in Fig. 8(a-b). The dimensions of straight crossed nanochannel for the simulation has been started from 1 nm radius and 2 nm length. In nano meter range there was no simulation up to 54 nm radius for straight crossed nanochannels because of errors occurred in the simulation. The setup tool of the ANSYS was not accepting such a small size and giving the errors "Divergence detected in AMG solver: Pressure correction" (accuracy for radius up to 55 nm and length up to 0.99 µm), "Divergence detected in AMG solver: x-momentum" and "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" as discussed in above section. Same 784 boundary conditions were kept for this channel and similar changes were done but no simulation took place. The number of nodes and elements were changed many times in mesh analysis but all in vain and no simulation observed. Simulation was done only at 54.9 nm radius and 1 µm length with the warning and i.e. "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization". We can ignore this type of warning because of the data obtained. With this data all flow parameters could be determined and tested experimentally. In micrometer range the simulation was done with the same warning.
The number of nodes and elements were changed many times in mesh analysis but warning was there all the times. A strange type of error occurred for 100-999.9 nm radius with 100 mm length. In this error there was no mesh creation but still simulation was done. Actually these were abnormal dimensions for this channel. ANSYS should not have done the simulation but simulation was done. That error is shown in Fig. 9(a-d).  When we further increased radius and length in millimeter range at 5.1 mm radius and 100 mm length simulation was done without any error with the same boundary conditions. The contour of pressure for this simulation is presented in Fig. 10. With warning error simulation was done for straight crossed microchannel at 182.15 aspect ratio. Error free simulation was done for this microchannel at 19.6 aspect ratio. It means ANSYS work best with these dimensions and beyond for straight crossed microchannel. Summary of the data of each simulation is shown in Fig. 11. 785 number of nodes and elements were changed in mesh analysis by changing the relevance between 0-100. It could also be varied by changing minimum size, maximum size and maximum face size of the element used in sizing tool function of mesh analysis. In this function of mesh analysis relevance center and smoothing were set at fine and high respectively. Here, the function "Use Advanced Size Function" was also set on curvature. Design and mesh analysis for this nanochannel are shown in Fig. 12(a-b). This channel was square in shape from inlet and outlet. The simulation for this channel started for the dimensions 1nm (width and depth) and 10 nm in length. The error "Divergence detected in AMG solver: pressure correction" came up to 180 nm (width and depth) and 400 nm in length. If pressure was changed for correction, then the error changes to "Divergence detected in AMG solver: x-momentum". Therefore, no simulation was done. Only at 50 nm (width and depth) and 500 nm length, the error "1 solution is converged" came with no simulation. It is shown in Fig. 4 previously. If width and depth were increased up to 180.1 nm and still the length is 400 nm. Simulation was done with warning error "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization". With this warning first five iterations were obtained zero. But this error can be ignored because measurements of flow could be determined. Then length is decreased in order to obtain the minimum length for this channel for simulation. Hence, 398.2 nm length was obtained with the same value of width and depth and simulation was done.
Therefore, it was concluded that minimum width and depth were 180.1 and 398.2 nm length was suitable for simulation. There would be no simulation found below these dimensions. Warning error was still there. When the width and depth were increased up to 180 µm with the 180 µm length. There would be error free simulation. The contour of pressure for this simulation is shown in Fig. 13.

Fig. 13: Contour Pressure for Simulation
With warning error simulation was done for straight square microchannel at 2.21 aspect ratio. Error free simulation was done for this microchannel at 1.0 aspect ratio. Simulation was done beyond these dimensions without error. It means ANSYS work best with these dimensions and beyond for straight square microchannel. The summary of simulated data is shown in Fig. 14.

Curvilinear Nanochannel
Curvilinear channel is the channel in which there are at least two curves of the same radius. The motion of the fluid in that channel is in fixed curves and is called curvilinear motion. This nanochannel was also created and meshed in ANSYS design modeler and mesh analysis respectively. That is shown in Fig. 15(a-b).

Computer Simulation Based Optimization of Aspect Ratio for Micro and Nanochannel
Mehran The process of simulation started with channel radius 1 and 200 nm length. In mesh analysis the relevance was set at zero, relevance center was set at fine and smoothing was set at high. In model function of set up tool energy equation was checked. In the same function laminar viscous model and k-epsilon function was opted. From the materials tool water was selected as flowing fluid from the fluent database. Same boundary conditions and reference values were set as before used in this study. There was no simulation for 1-50 nm radius due to errors like "Divergence detected in AMG solver: pressure correction" and "Divergence detected in AMG solver: x-momentum" (accuracy for radius up to 50-180 nm and length up to 1.2-2.1 µm). When radius was increased slightly to 50.1 nm then simulation was done with a warning error "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization". The length was determined for the simulation and it was found 829 nm. The simulation was done with the same warning. Then radius and length was further increased for the error free simulation. Finally, the radius and length were found 22 and 209.1 µm respectively. Before these values of radius and length, simulation was done with the warning error. The contour of pressure for this simulation is shown in Fig. 16. Error free simulation was done for curvilinear microchannel at 9.50 aspect ratio. At these values and beyond error free simulation was done. The summary of this simulation in shown in Fig. 17. In this research work, a new type of error occurred again and again. Numerous simulations were done in this study again and again for longer duration of time. Therefore, ANSYS software gave the error "GuiOperation Edit". The error came when we closed design modeler and opened mesh analysis. This error also came when we closed mesh and opened set up. The error message is shown in Fig. 18. All ANSYS applications must be terminated for the elimination of above said error. There was a file in ANSYS folder named as v140 in local disk (c) of the computer. In this file there were all the ANSYS workbench configuration files. Due to the presence of these large number of files ANSYS worked slowly. We just had to rename it. This file was renamed from v140-140.old. Now all the configuration files in Workbench was hidden due to this technique. Then

Computer Simulation Based Optimization of Aspect Ratio for Micro and Nanochannel
Mehran

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ANSYS Workbench got the fresh start. New and fresh set of configuration files were generated this time. This technique worked best until the large number of files in ANSYS were built again. There is no permanent solution of this error. This error remains in the simulations. The supported graphics card and updated driver proved very necessary for the computer system to do the simulations.

RESULTS AND DISCUSSION
After all this long simulation work we have to summarize all the research work. In this novel research work, the software ANSYS is investigated in nano sized channels. We have considered straight channels and a curvilinear channel for the investigations. The errors "Divergence detected in AMG solver: pressure correction", "Divergence detected in AMG solver: xmomentum", "1 solution is converged", "GuiOperation Edit" and "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" are common in simulations. Amongst these errors "Divergence detected in AMG solver: pressure correction" and "Divergence detected in AMG solver: x-momentum" occurred due to the nano sized channels. ANSYS just cannot handle these sizes. In "units" function of design modeler tool, nano meter is not mentioned. The lowest unit used there is micrometer. There are 18 versions of ANSYS in market but there is no nanometer unit available in it. Therefore, ANSYS is not suitable for nano sized channels. However, nano sized object can be created in design modeler and also meshed in mesh analysis. The results are discussed below for each microchannel separately.

Simulation of Straight Circular Micro Nanochannel
It is found that there are limits for simulation in case of straight circular channel. The simulation of straight circular channel cannot be done when its radius and length are less than 299.9 nm and 3 µm. It means that if we take length in nano meter range then no simulation takes place. Therefore, simulation cannot be done in nano sized straight circular channel.
Simulation takes place when we increase radius and length up to 300 nm and 3.1 µm with one error and i.e. "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization". This warning is ignorable because all the measurements of fluid flow can be determined with this simulation. It works for 124.9 µm radius and 900 µm length without error. This means that complete range of micrometer is not suitable for simulation without error.

Simulation of Straight Crossed Micro/Nanochannel
In case of straight crossed microchannel simulation was done only at 54.9 nm radius and 1 µm length with the error of warning. No simulation takes place for the values lower than 54.9 nm radius and 1 µm length. The errors shown by the ANSYS are "Divergence detected in AMG solver: pressure correction" and "Divergence detected in AMG solver: x-momentum". When radius is increased up to 999.9 µm then simulation was done without meshing. All the values were obtained without channel figure in the "result" tool of the ANSYS. Therefore, this simulation was not trusted. With the further increase in radius and length up to millimeter range (5.1 mm radius and 100 mm length), then error free simulation was done. It means ANSYS has problems in micrometer and millimeter range in some microchannels.

Simulation of Straight Square Micro/Nanochannel
In case of straight square channel, there were no simulation up to 180 nm (width and depth) and 398.1 nm length. The same errors "Divergence detected in AMG solver: pressure correction" and "Divergence detected in AMG solver: x-momentum" are occurred. Simulation was done for 180.1 nm (width and depth) and 398.2 nm length with the same warning error. Error free simulation takes place for the value of 180 µm (width and depth) and 180 µm length. It means that ANSYS has simulation problems in this range with some channels.

Simulation of Curvilinear Micro/Nanochannel
In case of curvilinear channel, no simulation was done up to 50 nm radius. Same errors "Divergence detected in AMG solver: pressure correction" and "Divergence detected in AMG solver: x-momentum" are occurred. 788 warning error. Simulated length was found for this channel as 829 nm with the same warning error. In micrometer range error free and trusted simulations were done for 22 µm radius and 209.1 µm length and beyond.

Validation of CFD results
Dietrich et. al. [30] used straight square millimetric channel for their research and 180 µm (width and depth) and 180 µm length has been reported in this research. With high aspect ratio,150 µm width and 600 µm length rectangular microchannel was fabricated and tested by Campo and Greiner [31]. This aspect ratio is higher than our simulated aspect ratio. Wewala et. al. [32] used curvilinear microchannel with minimum and maximum inner radius was 100 and 1150 μm. The authors have reported just 22 µm radius and 209.1 µm length for better fluid flow.
The literature has no investigations for the least aspect ratio of micro/nano-channels. Researchers have been useing micro/nano-channels with higher aspect ratios. Therefore, validation of CFD results are not possible for all micro/nano-channels. In this study, the authors have simulated micro/nano-channels for better fluid flow.

The Issue of Errors
In these errors, when pressure was changed or corrected then message of x-momentum error was shown on the screen. When momentum was changed or corrected then the message of pressure correction error shown on screen. The other errors were "1 solution is converged", "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" and "GuiOperation Edit". The error message "1 solution is converged" meant no simulation. Fluid could not be entered channel with any desired values of pressure and velocity. The error "Warning: convergence tolerance of 1.000000e-6 not reached during Hybrid Initialization" occurred after the initialization in set up tool of ANSYS. It was investigated that the default number of iterations were not enough and we had to increase the number of iterations and re-initialize the flow. But when number of iterations were corrected then the above said errors occurred at nano meter range. With warning error, the first five iterations are zero in the result. The error when simulation was done without meshing was also very strange. This error occurred for any dimension of nanochannels. However, this type of error could be controlled by using correct mesh. Sometimes this error could not be controlled for a particular geometry and dimension of microchannels. The error of "GuiOperation Edit" occurred when ANSYS software is used again and again for many simulations. In order to get rid of these errors we have to change the geometry or the size of the channel. We cannot simulate our desired micro/nanochannel with desired dimensions in ANSYS.
Moreover, simulation encountered convergence failures when an imbalance geometry was used in ANSYS FLUENT. This failure meant that there was too much imbalance in the system. The calculated reaction forces did not match the applied loads. Although, ANSYS FLUENT tried hard to make the flow and overcome the imbalances, it has not been able to do so and stops. If force residuals under solution information was observed, then it meant that the solver has been unable to get the force convergence residual and imbalance force. Sometimes ANSYS has performed simulation for an imbalance geometry with no mesh or mesh error.

CONCLUSION
ANSYS FLUENT is used for each and every simulation. Some limitations are found in software simulation of different geometries of micro/nanochannel. Simulation depends upon some suitable aspect ratio of the channels and also on courant number. The simulation with more suitable dimensions of the micro/nano channels does not depend upon courant number. Moreover, simulation cannot be done due to the limitations of the software at nanometer range for different micro/nano-channel. There are total 18 versions of ANSYS but ANSYS Company has not considered this issue. ANSYS Company has not yet enhanced the capacity of simulation with all dimensions in nanometer range. The options of units are also same as eighteen years before. There is no nanometer unit in ANSYS as an option. The channels with all dimensions in nano