Finite Element Analysis · Heat Conduction · MATLAB / ABAQUS

Finite Element Heat Conduction Analysis of a Turbine Blade

A finite element analysis project solving a two-dimensional heat conduction problem in one-eighth of a turbine blade using Galerkin’s method, linear triangular elements, MATLAB implementation, and ABAQUS validation.

Tools

MATLAB, ABAQUS

Methods

Galerkin Method, FEM, Heat Transfer

Institution

Columbia University

Fine mesh temperature contour for turbine blade heat conduction — Temperature contour from the fine-mesh MATLAB FEM model.

ABAQUS fine mesh temperature contour for turbine blade — ABAQUS fine-mesh temperature contour used for validation.

Project Overview

This project analyzed heat conduction in a turbine blade section by taking advantage of symmetry and modeling one-eighth of the blade. The work derived the strong form, weak form, and finite element discretization of the heat conduction problem, then implemented the numerical solver in MATLAB using linear triangular elements.

The MATLAB results were compared against ABAQUS simulations under coarse and fine meshes. The comparison included temperature contours, normal heat flux, flux vector fields, and boundary-condition validation. The results show that the MATLAB implementation agrees well with ABAQUS, supporting the accuracy and feasibility of the Galerkin FEM solver.

Coarse Mesh 267 nodes

Coarse triangular mesh with 455 elements generated from ABAQUS.

Fine Mesh 1958 nodes

Fine triangular mesh with 2287 elements for convergence comparison.

Element Type Linear Triangles

Used three-node triangular elements with linear shape functions.

Validation MATLAB vs. ABAQUS

Compared temperature and normal flux results across meshes.

My Role

Derived the strong and weak forms for the heat conduction problem.
Implemented Galerkin finite element formulation using linear triangular elements.
Assembled the global stiffness matrix and force vector in MATLAB.
Computed temperature fields and heat flux vector fields for coarse and fine meshes.
Compared MATLAB numerical results with ABAQUS FEM simulations.
Analyzed mesh refinement, boundary-condition accuracy, and flux singularities near sharp geometry points.

Mesh Design

The turbine blade geometry was discretized using linear triangular elements. Both coarse and fine meshes were used to study convergence behavior and compare the sensitivity of temperature and flux fields to mesh density.

Coarse triangular mesh for turbine blade — Coarse mesh with boundary nodes and triangular elements.

Fine triangular mesh for turbine blade — Fine mesh used for convergence and validation.

Temperature & Flux Results

The temperature contours from coarse and fine meshes show similar thermal patterns, indicating convergence of the numerical solution. The normal flux results match the boundary condition trend well overall, while sharp geometry points create local singular behavior.

Temperature contour using coarse mesh — Temperature contour using the coarse mesh.

Normal flux comparison between calculated and boundary flux — Normal flux comparison for coarse and fine meshes.

MATLAB / ABAQUS Validation

To verify the MATLAB implementation, the same heat conduction problem was solved in ABAQUS. The temperature and heat flux contours from ABAQUS were compared with the custom MATLAB FEM results under both coarse and fine mesh settings.

Coarse mesh temperature validation between MATLAB and ABAQUS.

Coarse mesh normal flux validation between MATLAB and ABAQUS.

Fine Mesh Validation

Fine mesh validation was used to further compare the MATLAB Galerkin FEM solver against ABAQUS. The fine mesh results provide a clearer view of convergence and improve the spatial resolution of both temperature and heat flux fields.

Fine mesh temperature validation between MATLAB and ABAQUS.

Fine mesh normal flux validation between MATLAB and ABAQUS.

Algorithm Design

The MATLAB solver was organized into pre-processing, analysis, and post-processing steps. The workflow included loading mesh connectivity and node locations, computing local stiffness matrices and force vectors, applying boundary conditions, assembling the global system, and solving for temperature and flux fields.

Bandwidth diagrams for global stiffness matrix — Bandwidth diagrams showing sparsity behavior of the stiffness matrix.

Flux field diagram with coarse mesh — Flux vector field computed on the coarse mesh.

Project Gallery

Mesh diagrams, temperature contours, flux fields, and MATLAB / ABAQUS validation results.

Temperature results comparison between coarse and fine meshes — Temperature comparison between coarse and fine mesh solutions.

Flux field diagram with fine mesh — Flux vector field computed on the fine mesh.

ABAQUS coarse mesh flux contour — ABAQUS coarse mesh heat flux contour.

ABAQUS fine mesh flux contour — ABAQUS fine mesh heat flux contour.