Orifice Plate: Single and Multi-Stage Pressure Drop

The orifice plate is a canonical internal flow benchmark for pressure drop across a constriction. This case sweeps four configurations of increasing complexity: a single plate with one centered opening, a single plate with three evenly spaced openings, and two- and three-plate staggered arrangements where the openings alternate between the upper and lower channel to force a serpentine flow path.

These configurations have direct industrial applications in flow metering (ISO 5167 orifice plates), labyrinth seals in turbomachinery, baffled heat exchangers, and muffler/silencer systems. The multi-stage cases provide a clear validation target: the total loss coefficient should scale approximately as N times the single-plate loss, with additional turning losses from the serpentine path.

Setup

Parameter Value
Grid 1600 × 1000
Configurations 1p1h, 1p3h, 2p, 3p
Plate thickness 8 cells (max(4, NX/100))
Hole width 125 cells (NY/8)
Reynolds number 100
Inlet velocity uinflow = 0.025 lu/ts
Tau (relaxation parameter) 1.25
Number of steps 30,000
Reference length H = NY = 1000 cells (channel height)
Collision MRT (d'Humieres 2002)
Boundary condition Zou-He inlet, convective outlet, bounce-back plates
Lattice spacing / time step Δx = 1, Δt = 1

Flow Field

Use the tabs below to select a parameter variant. Top left: steady-state velocity contour with streamlines. Top right: flow evolution from rest to steady state. Bottom: pressure and vorticity fields at steady state.

Velocity (Contour | Streamlines)

Contour Streamlines
Contour
Streamlines

Drag the handle to wipe between the velocity-magnitude contour and the streamline plot.

Flow Evolution

Frame 0 / 50

Pressure Coefficient Cp

Cp

Pressure Coefficient Cp

Vorticity

Vorticity

Vorticity

Validation

Config Re Computed Fx Loss Coeff K Regime
1 plate, 1 hole 100 13.1 139 Classic single orifice
1 plate, 3 holes 100 0.97 10.4 Perforated baffle (lowest loss)
2 plates 100 30.4 324 Single serpentine turn
3 plates 100 54.0 575 Double serpentine turn (highest loss)
The loss coefficient K represents the dimensionless pressure drop: K = 2 × Delta_p / (ρ × u2). For N plates with identical openings, the total loss should scale as K_total ≈ N × K_single (independent additivity) with additional losses from the serpentine turning flow. At Re=100 (laminar regime), viscous losses dominate and K scales as 1/Re. Reference: ISO 5167, Idelchik 2006 (Handbook of Hydraulic Resistance).

Discussion

The staggered orifice plate configuration exercises the solver's ability to handle multiple internal solid boundaries with confined flow passages. Unlike external aerodynamics cases where the flow can freely divert around obstacles, the serpentine path forces the fluid through narrow gaps at alternating elevations. This creates a complex flow pattern with:

The pressure drop across each stage depends on the contraction ratio (hole area / channel area), the Reynolds number, and the inter-stage spacing. For design purposes, the total loss is approximated as:

K_total = N × K_orifice + (N - 1) × K_turn

where K_orifice is the single-orifice loss coefficient and K_turn accounts for the 180-degree turning loss between stages. At high Re, K_turn dominates due to momentum-driven separation; at low Re (laminar), viscous friction in the inter-stage passages adds significant losses. This case serves as a validation bridge between simple orifice metering (ISO 5167) and complex labyrinth seal flows in turbomachinery.