Computational Fluid Dynamics(CFD) – Basics & How it Evolved

CFD Effectiveness = Quality x Acceptance
where,
Quality – Fidelity of Data
Acceptance – Timeliness of Data

CFD should essentially meet 3 requirements:
I. Rapid Turnaround.
II. Reliable Accuracy.
III. Affordable Cost.

A typical design process includes:
i. Pre-conceptual
ii. Conceptual
iii. Preliminary
iv. Critical
v. Production

I. Linear Potential Methods

  • Solve 1st order PDE
  • Based on Prandtl-Glauert /Laplace equation.
  • Green’s Theorem
  • Surface Discretization
  • Vortex-Lattice Methods (VORLAX code). Mean surface representation of geometry & vortex filaments as singularities.
  • Panel Methods (Actual surface geometry discretized)
  • Purely Subsonic & Supersonic flows.
  • Good estimate of F & M and distributed air loads for steady-level flight.
  • 1960’s, established 1980’s.

II. Non-Linear Potential Methods

  • Solver 2nd order PDE
  • Based on Transonic Small Perturbation (TSP) or Full Potential Equation ( FPE).
  • Benefit of modelling transonic flows with Shocks.
  • Need to solve non-linear PDE’s.

III. Euler Methods

  • Highest level of Inviscid approximations.
  • Subsonic to Hypersonic regimes.
  • Captures Potential flow regimes (Wake sheds from wing & leading edges)
  • Solving atleast 4 and generally 5 coupled 1st order PDE’s instead of one 2nd order PDE.
  • 1980’s : Structured Grid Generation, Patched Multiblock, Overset Mesh
  • Mid 1980’s : Unstructured grid generation.
  • Convergence acceleration techniques- i) Local time-stepping, ii) Multi-Grid (FMG)
  • Explicit and Implicit time-marching schemes.
  • Time dependent equations
  • Codes didnot provide Total Drag (incl. Skin Friction) and thus N-S codes were pursued in parallel.

IV. Navier-Stokes Method

  • Same equation except the diffusion terms in N-S solver
  • Elimination of the diffusion term converts the N-S equations to Euler equations as they both share some convective terms.
  • RANS- Turbulence Model – Simple algebraic model to sophisticated Reynolds’ Stress model.

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