Rocket Nozzle CFD.

The objective was to model expansion through a solid rocket motor nozzle, resolve the supersonic plume, and estimate thrust from the nozzle-exit flow properties.

The AeroTech J350W provided a commercial motor with reference thrust data for comparison. Our team used a simplified axisymmetric model to explore how the domain, mesh, boundary conditions, and numerical methods affected the result.

What the study brought together

• Geometry simplification and external-domain sizing.
• A grid study with nozzle-exit quantities and mesh-quality metrics.
• Chamber-pressure estimates and pressure-inlet conditions.
• Solver and turbulence-model selection for compressible flow.
• Thrust calculation and comparison with a published peak value.

The initial domain included the internal combustion chamber and a large surrounding region. Early runs showed that this added computational cost without improving the flow resolution near the exit.

The team removed the combustion chamber and applied a pressure inlet directly at the nozzle entrance. A half-section, treated as axisymmetric, retained the rotational geometry while reducing the computational problem to two dimensions.

A smaller external region

The surrounding domain was reduced while retaining space for plume expansion. A region above the nozzle allowed the exhaust’s interaction with ambient air to appear in the solution.

The boundary layout distinguishes the inlet, solid walls, symmetry axis, farfield region, and pressure outlets. Combustion itself was outside the model: inlet conditions represented its effect on the nozzle flow.

The team documented 17 mesh versions, adjusting element type, edge sizing, and biasing. Critical regions included the throat, nozzle exit, and expanding plume. The final approach favored quadrilateral elements and a structured multizone mesh.

Quality checks included aspect ratio, skewness, and orthogonal quality. Local throat sizing reached 0.1 mm in the study, while reducing the external domain helped control the overall element count.

Comparing the flow across meshes

The grid study examined Mach number along the centerline and velocity, pressure, and density at the nozzle exit. Averaged exit quantities and thrust provided another view of how the solution changed with element count.

Mesh 2, identified as iteration 13, was selected at approximately 142,000 elements. Its continuity residual had not converged during the grid-study stage; the team retained it and continued changing solver settings. The final residual history appears in the solver section below.

The inlet required chamber pressure and temperature representative of motor operation. The report used OpenMotor’s White Lightning propellant data to support estimates, then explored three methods for chamber pressure.

The team first tried a pressure-based solver, then moved to a density-based solver for the highly compressible flow. Although the latter improved the flow representation, convergence and computational cost remained difficult.

The final setup returned to a pressure-based coupled solver with realizable k–epsilon turbulence modeling, the energy equation enabled, and second-order upwind discretization. Spalart–Allmaras and the Reynolds Stress Model were also tested; the report describes tradeoffs in shock resolution, speed, and stability.

The final numerical configuration

• Solver: pressure-based, coupled scheme.
• Turbulence: realizable k–epsilon.
• Discretization: second-order upwind for the transported variables.
• High-order term relaxation: 0.1.
• Controls: 0.5 for pressure, momentum, and density; 0.85 for turbulent kinetic energy and dissipation; 0.65 for energy.

The final report describes improved residual behavior and resolved shock diamonds. The history above records that behavior directly; the report does not provide a numerical residual acceptance threshold or a separate mass-balance check.

The final Mach contour shows acceleration through the converging-diverging nozzle and repeating shock structures in the external plume. Pressure decreases as the flow expands.

Reported nozzle-exit quantities

The exit profiles below show how velocity and pressure vary across the section. The calculation above uses averaged quantities, so it is an approximation to an integrated momentum-and-pressure thrust evaluation.

These are simulation results and a reference-data comparison. This project did not document a new static-fire test of the motor.

The study demonstrated a practical workflow for building and improving a compressible-flow model. Its result depends on several deliberate simplifications:

• Steady state: the simulation does not follow pressure and thrust throughout the burn.
• Fixed inlet conditions: combustion and propellant regression are represented through boundary inputs.
• Air as the working fluid: the fluid properties do not exactly match the motor’s combustion products.
• Axisymmetry: asymmetric and three-dimensional behavior is excluded.
• Reference-based pressure: the peak-thrust comparison is linked to an inlet estimate informed by thrust data.

Where the model could go next

The report proposes transient analysis, combustion modeling, more representative exhaust-gas properties, and three-dimensional geometry. Further verification could also include consistent convergence criteria, mass balance, and a grid study repeated with the final solver configuration.

The original 22-page PDF contains the geometry development, grid study, chamber-pressure estimates, solver configuration, results, references, and appendix plots.

All 21 embedded images are included below, including individual panels from multi-part figures. Select an image to open it at full size. Page links use PDF page numbers, which are one higher than the report’s printed numbering after the cover.