Internal Flow & Pressure Loss

What Is It?

Internal flow CFD analyses the flow of fluid through confined passages — ducts, pipes, manifolds, plenums, diffusers, bends, valves and cooling passages. Unlike external aerodynamics, the flow is bounded by walls on all sides. The primary engineering quantities are the pressure loss (the pressure drop through the passage), the flow distribution (how the flow splits or combines), and the flow features (separation, recirculation, secondary flow) that affect performance. Internal flow CFD is widely used for engine intakes, cooling systems, HVAC, piping networks and hydraulic systems.

Why It Matters

Pressure loss through internal passages directly affects system performance — the pressure drop determines the pumping power required, the flow rate achievable and the system efficiency. Flow distribution affects whether all branches receive the intended flow. Recirculation and separation reduce the effective flow area, create dead zones and can cause thermal problems in cooling passages. Understanding how the flow features relate to the pressure loss and the flow distribution is essential for designing efficient internal flow systems.

Pressure loss is often created by local flow structure, not just straight-pipe friction. A bend, a junction, a sudden expansion or a valve creates local separation and recirculation that contributes more to the pressure loss than the straight-pipe friction. CFD captures these local losses that empirical correlations may miss.

Mass Conservation in Internal Flow

In internal flow, mass conservation is fundamental — the mass flow rate is constant through the system (for steady flow with no leakage). At a junction or branch, the mass flow splits: the sum of the mass flows in the branches equals the mass flow in the main. This conservation is enforced by the CFD solver, but it should also be checked as a verification — the mass flow at each section should be consistent with the intended design. A mass imbalance indicates a numerical problem or a leakage in the model.

Pressure Drop and Velocity Distribution

The pressure drops through an internal passage due to friction (wall shear stress) and local losses (separation, recirculation, geometry changes). The pressure drop is the difference between the inlet and outlet pressures. The velocity distribution through the passage shows where the flow accelerates and decelerates — in a duct contraction, the velocity increases; in a diffuser, the velocity decreases. If the diffuser angle is too aggressive, the flow separates from the walls and the pressure recovery is lost. The velocity distribution reveals these features and their effect on the pressure loss.

Darcy–Weisbach and Friction Loss

The Darcy–Weisbach equation gives the pressure drop due to friction in a straight pipe. It relates the pressure drop to the friction factor, the length-to-diameter ratio and the dynamic pressure. The friction factor depends on the Reynolds number and the relative roughness, and is typically obtained from the Moody chart or empirical correlations. The Darcy–Weisbach equation gives the friction loss for a straight pipe — it does not account for local losses from bends, junctions, valves or area changes.

Darcy–Weisbach equation (straight pipe friction loss):

Δp  =  f · (L/D) · (ρ V² / 2)

where:
Δp  =  pressure drop
f   =  Darcy friction factor (function of Re and relative roughness)
L   =  pipe length
D   =  pipe diameter (or hydraulic diameter for non-circular ducts)
ρ   =  fluid density
V   =  mean velocity

Note: this gives friction loss only — local losses (bends, junctions, valves) are additional

Minor / Local Losses

Local losses are pressure drops caused by geometry changes — bends, junctions, expansions, contractions, valves and other features. Each local feature creates a loss coefficient K that relates the pressure drop to the dynamic pressure. The total pressure loss is the sum of the friction losses (Darcy–Weisbach) and the local losses (K × dynamic pressure for each feature). In many internal flow systems, the local losses dominate — a sharp bend or a sudden expansion can create more pressure loss than a long straight pipe. CFD captures the local losses directly — the pressure drop through a bend, a junction or a diffuser is computed as part of the flow solution, without needing empirical loss coefficients.

Local (minor) loss:

Δp_local  =  K · (ρ V² / 2)

where:
K  =  loss coefficient for the specific geometry (bend, junction, expansion, valve)

Total pressure loss:

Δp_total  =  Δp_friction  +  Σ Δp_local

CFD computes Δp_total directly from the flow solution

Separation, Recirculation and Secondary Flow

Internal flows can develop several flow features that affect performance. Separation occurs when the flow leaves the wall — typically at sharp bends, sudden expansions or aggressive diffusers. Recirculation zones form behind separation points — regions of reversed flow that reduce the effective flow area and create dead zones. Secondary flow is flow perpendicular to the main flow direction — it occurs in bends (the Dean vortices) and in non-circular ducts. These features increase pressure loss, reduce flow uniformity and can cause thermal problems (hot spots in cooling passages). CFD captures these features, allowing the engineer to identify and address them.

Developing Flow

In a straight pipe, the flow develops from the inlet to a fully developed profile — a parabolic profile for laminar flow or a power-law profile for turbulent flow. The development length is the distance over which the flow reaches the fully developed state. If the inlet or outlet of the CFD domain is within the developing region, the pressure loss and the velocity profile at the boundary will not represent the fully developed flow. The domain should extend far enough upstream and downstream that the flow is fully developed at the boundaries, or the inlet profile should be specified to match the expected developing flow.

Mass-Flow vs Pressure-Driven Boundary Conditions

Internal flow can be driven by specifying the mass flow at the inlet (and the pressure at the outlet) or by specifying the pressure at both inlet and outlet (the pressure difference drives the flow). The choice depends on the physical situation. If the system is driven by a pump delivering a known flow rate, the mass-flow boundary is appropriate. If the system is driven by a known pressure difference (e.g. between two reservoirs), the pressure boundary is appropriate. The results — the velocity, the pressure distribution, the pressure loss — depend on which boundary condition is used, and the choice should match the physical driving mechanism.

Key Takeaways

• Internal flow CFD analyses pressure loss, flow distribution and flow features in confined passages
• Pressure loss comes from friction (Darcy–Weisbach) and local losses (bends, junctions, expansions)
• Local losses often dominate — a bend or expansion can create more loss than straight-pipe friction
• Separation, recirculation and secondary flow increase pressure loss and reduce flow uniformity
• Mass-flow or pressure-driven boundaries should match the physical driving mechanism