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Finite-Inertia Eccentric Annular Navier-Stokes CFD Calculator

Solve coupled cross-sectional Navier-Stokes velocity and relative pressure in a rotating eccentric annulus with mesh, momentum and energy checks.

Inputs

Results

Calculate to view linked results. Default values are examples, not recommended operating inputs.

Local native models

A separate native OpenFOAM workflow covers 3-D RANS rectangular ducts, a different geometry and turbulence model from this low-Re annular cross section.

Local simulation workbench

Learn, compare and practice

Worked explanations, controlled studies and printable exercises connected to this calculation.

Mesh convergence and residuals in an annular CFD calculation

Calculation sequence

  1. Specify one uniform annulus, constant Newtonian viscosity and density, rotating inner wall and constant axial pressure drive. Offset is centre displacement divided by Ro-Ri. The radius ratio must be 0.3-0.8 and normalized offset 0-0.6. At least one drive must be nonzero. Rotational Re=rho*omega*Ri*(Ro-Ri)/mu must not exceed 10 before the solver loads.
  2. Solve a mixed finite-element system for both cross-sectional velocities, axial velocity and pressure. The nonlinear convective coefficient is updated iteratively; no independent axial/rotational superposition is used. Skew convection supports a mechanical energy audit. The pressure gauge fixes one degree of freedom and must not be interpreted as an absolute-pressure boundary condition.
  3. Compare 6x48 and 10x80 radial/angular annular meshes. Reject flow or torque refinement change above 2.5%, failed nonlinear or residual checks, or a combined nodal-speed Reynolds screening number above 20. Polygonal boundary and discretization errors are included in that numerical comparison; it is not a rigorous error bound or a flow-stability proof.
  4. Inspect the axial velocity, speed and relative-pressure fields, then compare narrow/wide gap profiles. Field samples come from the solved P2 velocity nodes and interpolated P1 pressure, not a fabricated image. Field CSV exports the displayed samples. Main CSV/PDF retain the gap profiles and all stated assumptions. Increase density within the supported domain to exercise inertia; use zero offset for analytical concentric checks.
  5. Calculation stays in a dedicated local WebAssembly worker. The scientific engine is downloaded only on calculation; CFD additionally loads the existing hash-verified 178 KB finite-element package. No composition or field is sent to a calculation server. Save stores canonical inputs in this browser. Download its file backup from Saved work to protect it from browser-storage loss or share it with colleagues; reopening recalculates with the current formulas. CSV/PDF retain reported profiles and assumptions; the separate field CSV retains displayed CFD field samples.

Worked check

The synthetic default has Ri=0.05 m, Ro=0.10 m, 40% eccentricity, viscosity 0.05 Pa.s, density 1000 kg/m3, rotation 0.1 rad/s and G=0.5 Pa/m over 1 m. It returns about 0.0000602936614 m3/s axial flow, 0.000233914127 N.m drive torque and 0.0000535382434 W combined power. Rotational Re is 5 and the flow/torque mesh change is about 0.369%. Setting eccentricity to zero permits comparison with analytical concentric axial flow, rotational torque and centrifugal pressure. These are verification configurations, not a drilling-fluid recommendation.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

  • Steady, fully developed, isothermal, incompressible Newtonian flow on one 2-D cross-section with three velocity components. No axial variation except constant pressure gradient, no ends/inlet development and no moving mesh.
  • Rotational Re<=10, combined nodal-speed Re<=20; these are conservative numerical screening limits, not claimed transition or Taylor-instability boundaries. No 3-D Taylor vortices, turbulence or turbulent wall function is resolved.
  • No non-Newtonian fluid, cuttings, beds, gas/liquid interface, VLLS transport, compressibility, heat transfer, erosion, wall slip, axial pipe translation or time evolution. The separate creeping HB workflow retains yield-stress rheology but omits inertia.
  • Mesh/refinement and conservation checks do not establish experimental accuracy, mesh independence for all parameters, operational fitness or certified engineering review. Field pressure is relative to an arbitrary fixed pressure degree of freedom.

Implemented equations

Three-component finite-inertia momentum

ρ(u⊥⋅∇⊥)u=−∇⊥p+∇⊥ ⁣⋅(2μD)+Gez∇⊥ ⁣⋅u⊥=0\begin{gathered}\rho(\mathbf u_\perp\cdot\nabla_\perp)\mathbf u\\=-\nabla_\perp p+\nabla_\perp\!\cdot(2\mu D)\\\quad+G\mathbf e_z\\\nabla_\perp\!\cdot\mathbf u_\perp=0\end{gathered}

Discrete mechanical energy audit

GQ+ωT=∫Ω2μD:D dA\begin{gathered}GQ+\omega\mathcal T\\=\int_\Omega 2\mu D:D\,dA\end{gathered}

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: . This does not claim independent expert review.

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