Submarine Design Optimization: RBF Morph (Adjoint Solver)

Submarine Design Optimization using Adjoint Solver (RBF Method), ANSYS Fluent

Description

When a structure moves at a given speed through a continuous fluid, its body experiences forces from that fluid — as with a submarine moving through water, where hydrodynamic forces act on its surface. One of the most significant of these is drag force, acting horizontally against the submarine's direction of travel and creating resistance to its motion.

Minimizing drag is a key consideration in submarine design and construction, with the magnitude of drag force depending directly on the geometric shape and dimensions of the hull. This project applies an optimization process to the submarine's geometry to reduce drag using CFD analysis.

Several optimization methods exist for shape design, and ANSYS Fluent provides an adjoint solver tool specifically for geometric optimization — capable of iteratively adjusting target geometry dimensions through a structured solution process until an optimal shape is achieved.

This simulation applies adjoint-solver-based optimization to reduce drag force across three stages: first, a baseline simulation is run on a standard submarine geometry to establish initial drag; second, the adjoint solution identifies which regions of the submarine's geometry are most sensitive to drag force; and third, optimization is performed to reduce the target drag value by a defined percentage.

The 3D geometry — a simple submerged submarine — was modeled in Design Modeler and meshed in ANSYS Meshing using an unstructured grid of 258,938 cells.

Methodology

The submarine's configuration is optimized based on drag force reduction. An initial simulation establishes the baseline drag by modeling water flow around the submarine. The Design tab handles the optimization process itself.

Drag force is first defined as the target quantity, followed by selecting discretization methods for the adjoint solver in the Method section. Running the adjoint solution then yields a shape sensitivity distribution, identifying which regions of the geometry most strongly influence drag.

The final optimization step uses the Design tool with the polynomial morphing method, again selecting drag force as the objective. A target percentage decrease is specified, and a bounded region around the model is defined to constrain geometric changes to that space. The optimization itself runs through the gradient-based optimizer.

Result

The baseline drag force measured 11.485855 N; following adjoint-solver optimization, this dropped to 6.4377518 N — a 44% reduction, confirming the optimization was successfully applied.

This reduction stemmed from geometric changes to the hull dimensions, examined using the iso-clip tool to compare pre- and post-optimization geometry. In cross-section, dimensions shifted from 0.5066175×0.5063399 to 0.4386431×0.453043; in the side profile, from 4.353052×0.6 to 4.09195906×0.5952543.

Since drag force correlates directly with cross-sectional area, the reduced cross-section directly explains the drag decrease. Total drag force is the sum of pressure drag and frictional drag: pressure drag arises from the pressure differential across the submarine's two sides — smaller cross-sections reduce this differential — while frictional drag depends on side surface area, meaning reduced surface area lowers frictional resistance as well.