Instructor! Flow analysis in ducts is used for HVAC and plant piping systems, right? Could you explain the basics?

CFD analysis of duct flow is performed to predict pressure loss, flow distribution, and flow maldistribution in piping and duct systems. At the design stage, CFD visualizes local losses and secondary flows that cannot be fully captured by manual calculations using the Darcy-Weisbach equation alone.

The fundamental equation for pressure loss is Darcy-Weisbach, correct?

Yes. The frictional loss in straight pipe sections is described by the Darcy-Weisbach equation: $$ \Delta p_f = f \frac{L}{D_h} \frac{\rho V^2}{2} $$

While loss coefficients for manual calculations come from literature, CFD can provide accurate values specific to the geometry, right?

Correct. Especially for components like corner pieces in rectangular ducts or complex branch pipes, literature values are often unavailable, making CFD valuable for determining them.

What turbulence model is suitable for duct flow analysis?

The Realizable $k$-$\varepsilon$ model is standard for internal pipe flows. Enhanced Wall Treatment (y+ ≈ 1) is ideal for wall functions, but the Standard Wall Function (y+ = 30–300) also provides practical accuracy for pressure loss prediction. | Turbulence Model | Recommended Use | Remarks | |---|---|---| | Realizable k-epsilon | Straight pipes, elbows | Versatile, fast computation with wall functions | | SST k-omega | Separation, sudden expansion | Strong for adverse pressure gradients | | RSM (Reynolds Stress) | Swirling flow, secondary flows | High accuracy but high computational cost |

Flow in Ducts

Category: Fluid Analysis (CFD) | Integrated 2026-04-06

Duct Flow

Flow in Ducts: Theoretical Foundations

Overview

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Teacher! The analysis of flow inside ducts is the one used for HVAC piping and plant piping, right? Please teach me from the basics.

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CFD analysis of duct flow aims to predict pressure loss, flow distribution, and flow maldistribution in piping and duct systems. At the design stage, it visualizes local losses and secondary flows that cannot be fully captured by hand calculations using the Darcy-Weisbach equation alone.

Governing Equations

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The basic formula for pressure loss is the Darcy-Weisbach equation, right?

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Yes. Frictional loss in straight pipes is described by the Darcy-Weisbach equation.

$$ \Delta p_f = f \frac{L}{D_h} \frac{\rho V^2}{2} $$

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Here, $f$ is the pipe friction factor, $L$ is the pipe length, $D_h$ is the hydraulic diameter, and $V$ is the cross-sectional average velocity. For laminar flow, $f = 64/Re$, and for turbulent flow, it is obtained from the Colebrook equation.

$$ \frac{1}{\sqrt{f}} = -2.0 \log\left(\frac{\varepsilon/D_h}{3.7} + \frac{2.51}{Re\sqrt{f}}\right) $$

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The Colebrook equation is implicit, so iterative calculation is needed. In practice, is the Swamee-Jain approximation often used?

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Exactly. Swamee-Jain is explicit and has sufficient accuracy for practical use.

$$ f = \frac{0.25}{\left[\log\left(\frac{\varepsilon/D_h}{3.7} + \frac{5.74}{Re^{0.9}}\right)\right]^2} $$

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Local losses (elbows, branches, expansions/contractions) are expressed using a loss coefficient $K$.

$$ \Delta p_{local} = K \frac{\rho V^2}{2} $$

Element	Loss Coefficient K (Guideline)
90° Elbow (R/D=1.5)	0.2~0.3
90° Miter (No Vanes)	1.1~1.3
T-Junction (Straight Through)	0.3~0.5
T-Junction (Branch)	0.8~1.3
Sudden Expansion	$(1 - A_1/A_2)^2$
Sudden Contraction	$0.5(1 - A_2/A_1)$

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Loss coefficients in hand calculations are from literature values, but with CFD, you can get accurate values specific to the geometry, right?

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Yes. Especially for rectangular duct corner pieces and complex branch pipes, literature values are often unavailable, so it's valuable to obtain them via CFD.

Turbulence Model Selection

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What turbulence model is suitable for duct flow?

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For pipe flow, the Realizable $k$-$\varepsilon$ model is standard. For wall functions, Enhanced Wall Treatment (y+ ≒ 1) is ideal, but even with Standard Wall Function (y+ = 30~300), pressure loss prediction achieves practical accuracy.

Turbulence Model	Recommended Application	Notes
Realizable k-epsilon	Straight pipes / Elbows	General purpose, fast calculation with wall functions
SST k-omega	Separation / Sudden expansion	Strong against adverse pressure gradients
RSM (Reynolds Stress)	Swirling flow / Secondary flow	High accuracy but high computational cost

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Secondary flow (corner vortices) occurs in rectangular ducts, can it be captured with k-epsilon?

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Secondary flow in rectangular ducts originates from Reynolds stress anisotropy, so strictly speaking, RSM is needed. However, if the purpose is pressure loss prediction, k-epsilon can keep the error within about 5%.

Coffee Break Yomoyama Talk

The Theory of "Entry Length" — How Many D from the Duct Inlet Until Turbulent Flow is Fully Developed?

The first important concept learned in duct flow theory is the "hydrodynamic entry length." It refers to the distance from the inlet until the flow, influenced by the wall boundary layer, becomes a fully developed turbulent profile across the entire cross-section. For turbulent flow, approximately $x \approx 10 \sim 60 D$ (relative to diameter D) is required. A common mistake in practical CFD analysis is "setting the inlet condition as uniform flow while making the analysis domain just barely long enough." Unless sufficient entry length is secured or a measured velocity profile is set as the inlet condition, pressure loss downstream tends to be underestimated.

Computational Methods for Flow in Ducts

Details of Numerical Methods

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When solving duct flow with CFD, what should I be careful about regarding mesh and boundary conditions?

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Let's start by explaining the mesh.

Mesh Strategy

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Does the mesh creation method change between circular pipes and rectangular ducts?

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It changes significantly. For circular pipes, O-grid topology (bow-tie type) is recommended, as it easily ensures prism layers orthogonal to the wall. For rectangular ducts, use sweep mesh with prism layers.

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The height of the first layer at the wall should match the wall model used.

Wall Model	Required y+	First Layer Height Guideline (Re=10⁵, D=300mm)
Enhanced Wall Treatment	≒ 1	Approx. 0.05 mm
Standard Wall Function	30~300	1~10 mm
Scalable Wall Function	> 11.225	> 0.4 mm

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Setting y+ = 1 increases the cell count considerably. From a pressure loss accuracy perspective, are wall functions sufficient?

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For frictional loss in straight pipes alone, wall functions are sufficient. However, for sudden expansions with separation or behind valves, wall resolution (y+ ≒ 1) yields higher accuracy.

Boundary Condition Settings

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How do you set the inlet/outlet boundary conditions?

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Here are typical setting patterns.

Boundary	Condition Type	Setting Value
Duct Inlet	Velocity Inlet	Design air velocity + Turbulence intensity 5%, Hydraulic diameter
Duct Outlet	Pressure Outlet	Gauge pressure 0 Pa
Fan Location	Fan BC (Pressure Jump)	Fan characteristic curve
Damper	Porous Jump	Resistance coefficient according to opening
Wall	No-Slip Wall	Roughness height (Steel pipe: 0.045 mm)

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So you input wall roughness into CFD. Where can I look up roughness height for each material?

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Representative values are listed in ASHRAE Handbook Fundamentals and Crane TP-410.

Material	Equivalent Roughness [mm]
Galvanized Sheet Metal Duct	0.09~0.15
Steel Pipe	0.045
PVC Pipe	0.0015
Concrete Duct	0.3~3.0
Flexible Duct	1.0~4.6

Inlet Entry Length Treatment

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When assuming fully developed flow, how do you handle the entry length?

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The turbulent entry length is roughly $L_{entry} \approx 10 D_h$. If the purpose is not to evaluate pressure loss immediately after the inlet, either provide sufficient entry length or give a Fully Developed Profile as the inlet condition. In Fluent, another method is to use the Mapped condition at the inlet (a periodic condition that maps the outlet velocity profile to the inlet).

Solver Settings

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Please tell me the recommended specific solver settings.

Parameter	Recommended Setting
Solver	Pressure-Based, Steady
Pressure-Velocity Coupling	SIMPLEC
Convection Scheme	Second Order Upwind
Pressure Interpolation	Second Order
Gradient	Least Squares Cell-Based
Convergence Criterion	Residual below 1e-4 + Inlet/Outlet Flow Rate Balance < 0.1%

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Using the inlet/outlet flow rate balance for convergence judgment is practical. Relying on residuals alone might overlook...

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