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Numerical Optimization

Numerical Optimization is at the core of what our CFD consulting engineers do here at BroadTech Engineering in our Singapore offices.

Featured Numerical Optimization Case Studies

 numerical optimization

An investigation into Stresses Values of 20 x 20m plate Subjected to Axial Loading

Objective: Objective of the design optimization and structural validation related project is to investigate the principal stresses subjected to 20 x 20m plate consisting of a hole at the center subjected to axial loading.
Methodology Approach:
Due to the symmetry of the plate, only 1/4 of the plate was modeled. FEA finite element analysis was performed by our FEA consultants using Visual FEA Software. The approach consists of producing 3 models by keeping the loading and material properties constant. But changing the mesh concentration near the plate hole to investigate which model produced fluid flow analysis results closest to the results obtained from theoretical formulae.
Outcome & Results:
Observations of the FEA analysis were as the area of interest is the stresses near the hole, the no of integration points near this region should be changed to obtain more accurate finite element simulation (IL: Finite Element Simulation) results.
For all 3 FEA simulation models, the stress away from the hole converged to the theoretical values providing accurate values, however, drastic changes of the stress values were observed near the hole of the plate. The model with a higher refined mesh and greater integration point near the plate hole provided the most accurate values. However, this would increase no of degree of freedom which would result in more processing time. The requirements for the FEA consultancy project was to keep the degree of freedom within 60-80.

Thermal Radiation interaction with Buoyancy-Driven Flows in Square Enclosure with a Heated Cylinder

Objective of Simulation:
Numerical thermodynamics simulation to investigate the interaction of thermal radiation with buoyancy driven flows in a square enclosure with a heated cylinder are studied.
Three different configurations of heated cylinder viz. circular, square and triangular shapes are chosen for the steady-state thermal analysis and are placed at the center of the square enclosure.
Such configurations adopted for the transient thermal analysis are relevant in the thermal design of gas cooled reactors.
The objective of the CFD Modeling and FEM thermal analysis study is to present an optimum thermal design (high heat transfer rates with minimum entropy generation due to conduction, convection, and radiation. ) among the three geometries of the heated cylinder.
Methodology:
CFD simulations are carried out using an in-house three-dimensional FVM based numerical solver based on low-Mach number formulation on arbitrary polyhedral meshes. Thermal Analysis results obtained from the low-Mach number formulation are also verified from a compressible solver using OpenFOAM.
Outcome & Conclusion:
From the FEM modeling done as part of the thermal simulation, it is found that the square and the triangular cylinders have a higher local heat transfer rates compared to the circular cylinder due to enhanced heat transfer at the corners. Fluid dynamic analysis results from this CFD thermal analysis show that square geometry is the optimum design among the three geometries as it has the maximum heat transfer rates and minimum entropy generation due to convection, conduction, and radiation.

Simulation of Surface Micro-features to Attain Drag Reduction and Transition Delay

Objective of Project:
Boundary layer transition is very sensitive to several factors namely turbulence, surface finish and geometry/topology. The presence of a rough surface and one with poorly optimized shape greatly influence boundary layer transition onset.
Early transition onset results in an increased drag during the computational fluid dynamics simulation. Drag reduction and transition delay play a great role in aerospace as well as automotive applications. The purpose of my project was the use of micro-features on the surface of a flat plate to attain drag reduction and transition delay. These micro-features were inspired by the shark-skin and a topology optimization was conducted until these micro-features demonstrated drag reduction.
Methodology:
The micro-features on the shark-skin are sinusoidal shaped waves known as dermal denticles. These dermal denticles have an amplitude of 2-3 μm. To ensure that the CFD simulation accurately captures the influence of these micro-features, the mesh needed to have a very fine resolution. In order to capture these features, the first cell height was chosen so as to attain a constant  y+=0.1 was maintained along the length of the entire plate. CFD simulations were performed for a number of sinusoidal wave numbers ranging from 32 waves to 256 waves all along the length of the plate.
The following steps were undertaken to ensure that the fluid flow simulation was accurate:
1. A grid independence study was undertaken. The skin friction coefficient C_f was the parameter that was analyzed. Three different mesh densities were used namely comprising of 100k, 300k, and 500k elements. The grid independence study indicated that the fine mesh provided the most accurate CFD flow analysis results.
2. The computational fluid analysis result was validated against existing literature using the Transition SST  turbulence model in FLUENT.
3. The fluid dynamics simulation was conducted as a steady state RANS 2D simulation using the pressure-based solver.
4. To ensure that the Transition SST model accurately depicts real-world phenomenon for non-flat surfaces, a sinusoidal wavy surface was compared to existing experimental literature.
Once the validation was successful, several wave amplitudes were tested, and the amplitudes were successively reduced from  9 μm to 0.2 μm. As compared to the shark-skin, the mesh had sufficient resolution to simulate wave amplitudes of 0.2 μm which were ten times smaller than a normal shark-skin denticle.
Outcome and Conclusion:
The topology optimization of the flat plate surface and the use of micro-features such as the sinusoidal wavy surfaces have shown great promise and a theoretical drag reduction of 3% has been attained. The findings from this shape structural optimization formed a fundamental part of the project and gave impetus to the research conducted under the public government project.
The CFD analysis results from this research are currently being reviewed in one of the top peer-reviewed journals (Fluid Dynamics Research) are expected to be published within the next two months. Thus, in the present case, my research challenges the existing notion that non-flat surfaces increase drag and lead to early transition onset. An optimized topology in this case not only delays transition and leads to a reduction in drag as well.

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