Fan and Blower CFD
Theory and Physics
Overview
What's the difference between a fan and a blower?
They are distinguished by pressure ratio. Generally, a pressure ratio of about 1.1 or less (total pressure rise of several hundred Pa) is a fan, and about 1.1 to 1.3 is a blower. The flow can often be considered essentially incompressible, but in high-speed fans, the blade tip Mach number can exceed 0.5.
Fan Laws (Similarity Laws)
Are fan laws used in CFD as well?
They are essential in the 1D design stage. For geometrically similar fans, the following relationships hold.
$N$: Rotational speed, $D$: Diameter. If you create a performance map for one rotational speed with CFD, you can estimate performance at other speeds using the similarity laws. However, correction for Reynolds number effects is necessary.
Total Pressure and Static Pressure
For fan performance, should we look at total pressure rise or static pressure rise?
It depends on how the fan is used.
- Duct System: Evaluate by total pressure rise $\Delta p_t$ (ducts connected upstream and downstream)
- Free Discharge: Evaluate by static pressure rise $\Delta p_s$ (outlet is open)
- Free Inlet: Evaluate by fan static pressure
Do we also change the CFD boundary conditions accordingly?
Yes. For a duct system, simulate the system pressure loss with the outlet boundary condition. For free discharge, set the outlet to atmospheric pressure (0 Pa gauge static pressure). The operating point is the intersection of the actual system resistance curve and the fan characteristic curve.
Fundamentals of Noise Prediction
Can fan noise also be predicted with CFD?
Yes. Fan noise is divided into discrete frequency components (BPF: Blade Passing Frequency) and broadband components.
Discrete components are predicted with URANS, and broadband components are predicted with LES/DES+FW-H. Both Fluent and STAR-CCM+ have built-in FW-H solvers.
History of Fan Theory—From Rankine-Froude Momentum Theory to Prandtl Wing Theory
Fan aerodynamic theory shares the same history as propeller theory, starting with the Rankine-Froude (1865–1878) momentum theory. It is a simple model that treats the fan as a virtual, infinitely thin actuator disk imparting momentum to the fluid. Later, Prandtl's (1921) wing theory (relationship between lift and induced drag) combined with vortex rings led to the development of the "Vortex Lattice Method," enabling calculation of individual blade aerodynamic characteristics. The modern BEM (Blade Element-Momentum) method is a one-dimensionalized design tool based on this. By calibrating the lift and drag coefficients of blade elements using a combination of CFD results and actual measurements, reliable performance prediction is achieved. Fan CFD functions as the "inspector" of this classical theory; CFD results deviating from BEM predictions are interpreted as signs of either detailed shape effects or turbulence influences.
Physical Meaning of Each Term
- Temporal Term $\partial(\rho\phi)/\partial t$: Imagine the moment you turn on a faucet. At first, water comes out spluttering and unstable, but after a while, it becomes a steady flow, right? This "during the change" is described by the temporal term. The pulsation of blood flow from a heartbeat, or the flow fluctuation each time an engine valve opens and closes—all are unsteady phenomena. So what is steady-state analysis? It looks only at "after sufficient time has passed and the flow has settled down"—meaning setting this term to zero. Since computational cost drops significantly, trying a steady-state solution first is a basic CFD strategy.
- Convection Term $\nabla \cdot (\rho \mathbf{u} \phi)$: What happens if you drop a leaf into a river? It gets carried downstream by the flow, right? This is "convection"—the effect where fluid motion transports things. Warm air from a heater reaching the far corner of a room is also because the air, as a "carrier," transports heat via convection. Here's the interesting part—this term contains "velocity × velocity," making it nonlinear. That is, as the flow becomes faster, this term rapidly strengthens, making control difficult. This is the root cause of turbulence. A common misconception: "Convection and conduction are similar things" → They are completely different! Convection is carried by flow, conduction is transmitted by molecules. There is an order of magnitude difference in efficiency.
- Diffusion Term $\nabla \cdot (\Gamma \nabla \phi)$: Have you ever put milk in coffee and left it? Even without stirring, after a while, it naturally mixes, right? That's molecular diffusion. Now a question—honey and water, which flows more easily? Obviously water, right? Honey has high viscosity ($\mu$), so it flows poorly. Higher viscosity strengthens the diffusion term, making the fluid move "sluggishly." In low Reynolds number flow (slow, viscous), diffusion dominates. Conversely, in high Re number flow, convection overwhelms, and diffusion plays a supporting role.
- Pressure Term $-\nabla p$: When you push the plunger of a syringe, liquid shoots out forcefully from the needle tip, right? Why? Because the plunger side is high pressure, the needle tip is low pressure—this pressure difference becomes the force pushing the fluid. Dam discharge works on the same principle. On a weather map, where isobars are tightly packed? That's right, strong winds blow. "Where there is a pressure difference, flow is generated"—this is the physical meaning of the pressure term in the Navier-Stokes equations. A point of confusion here: "Pressure" in CFD is often gauge pressure, not absolute pressure. If results go wrong immediately after switching to compressible analysis, it might be due to mixing up absolute/gauge pressure.
- Source Term $S_\phi$: Heated air rises—why? Because it becomes lighter (lower density) than its surroundings, so it's pushed up by buoyancy. This buoyancy is added to the equation as a source term. Other examples: chemical reaction heat from a gas stove flame, Lorentz force acting on molten metal in a factory electromagnetic pump... These are all actions that "inject energy or force into the fluid from the outside," expressed by the source term. What happens if you forget the source term? In natural convection analysis, forgetting buoyancy means the fluid doesn't move at all—a physically impossible result like turning on a heater in a winter room but the warm air doesn't rise.
Assumptions and Applicability Limits
- Continuum Assumption: Valid for Knudsen number Kn < 0.01 (molecular mean free path ≪ characteristic length)
- Newtonian Fluid Assumption: Shear stress and strain rate have a linear relationship (non-Newtonian fluids require viscosity models)
- Incompressibility Assumption (for Ma < 0.3): Treat density as constant. For Mach number 0.3 and above, consider compressibility effects
- Boussinesq Approximation (Natural Convection): Consider density changes only in the buoyancy term, using constant density in other terms
- Non-applicable Cases: Rarefied gas (Kn > 0.1), supersonic/hypersonic flow (requires shock capturing), free surface flow (requires VOF/Level Set, etc.)
Dimensional Analysis and Unit Systems
| Variable | SI Unit | Notes / Conversion Memo |
|---|---|---|
| Velocity $u$ | m/s | When converting from volumetric flow rate for inlet conditions, pay attention to cross-sectional area units |
| Pressure $p$ | Pa | Distinguish between gauge and absolute pressure. Use absolute pressure for compressible analysis |
| Density $\rho$ | kg/m³ | Air: approx. 1.225 kg/m³ @20°C, Water: approx. 998 kg/m³ @20°C |
| Viscosity Coefficient $\mu$ | Pa·s | Be careful not to confuse with kinematic viscosity $\nu = \mu/\rho$ [m²/s] |
| Reynolds Number $Re$ | Dimensionless | $Re = \rho u L / \mu$. Criterion for Laminar/turbulent transition |
| CFL Number | Dimensionless | $CFL = u \Delta t / \Delta x$. Directly related to time step stability |
Numerical Methods and Implementation
MRF Method (Steady)
Is MRF sufficient for fan CFD?
MRF is sufficient for predicting the performance curve (P-Q characteristic). Connect the rotating and stationary domains with a GGI interface and add Coriolis and centrifugal forces to the rotating domain. Computational cost is almost the same as for a stationary field calculation.
What are the weaknesses of MRF?
It cannot capture unsteady interactions between blades and downstream structures. For example, pressure pulsations due to interference with motor struts or outlet guide vanes cannot be calculated with MRF.
Sliding Mesh (Unsteady)
In what cases is Sliding Mesh necessary?
How do you determine the time step for Sliding Mesh?
A guideline is 20 to 50 time steps per blade passage. For 7 blades at 3000 rpm, the blade passing period is 60/(3000×7) = 2.86 ms. Dividing this by 30 gives $\Delta t \approx 95 \mu s$.
Incompressible and Weakly Compressible
For fans, can compressibility be ignored?
If the blade tip Mach number is below 0.3, incompressible is sufficient. It can be calculated with OpenFOAM's simpleFoam (steady) or pimpleFoam (unsteady). For Mach numbers 0.3 to 0.6, it's better to consider weak compressibility, using CFX's compressible solver or Fluent's pressure-based Coupled Solver.
Fan-Specific Mesh Tips
What should I be careful about with fan meshing?
Axial fans often have long chords and small aspect ratios (span/chord). Also, the relative size of the tip clearance is often large, so the influence of tip leakage flow is significant. Ensure sufficient mesh density in the blade span direction. Also, because fan inflow velocity is low, y+ tends to become small; be careful not to make the wall's first layer too thin.
Generating P-Q Curves for Fan CFD—Multi-Point RANS Calculations and Handling the Stall Point
To generate a fan performance curve (P-Q curve: pressure-flow characteristic) with CFD, it is necessary to perform analyses at multiple flow rate conditions (typically 5–10 points). Convergence is easy near the design flow rate (Best Efficiency Point, BEP), but at low flow rates (partial flow region), stall cells (Rotating Stall) occur and a steady solution ceases to exist. To track this "beyond the stall point" with CFD, unsteady (URANS) analysis is required; steady RANS will diverge or converge to a non-physical solution. In practical P-Q curve generation, a common method is to analyze 2–3 points each in the low and high flow directions centered on the design point, and supplement the region below the stall point with experiments or 1D theoretical predictions. Also, individually tuning the Relaxation Factor for each flow condition is a practical technique for improving convergence.
Upwind Differencing (Upwind)
First-order upwind: Large numerical diffusion but stable. Second-order upwind: Improved accuracy but risk of oscillations. Essential for high Reynolds number flows.
Central Differencing
Second-order accurate, but numerical oscillations occur for Peclet number > 2. Suitable for low Reynolds number diffusion-dominated flows.
TVD Schemes (MUSCL, QUICK, etc.)
Maintain high accuracy while suppressing numerical oscillations via limiter functions. Effective for capturing shock waves or steep gradients.
Finite Volume Method vs Finite Element Method
FVM: Naturally satisfies conservation laws. Mainstream in CFD. FEM: Advantageous for complex shapes and multi-physics. Mesh-free methods like SPH are also developing.
CFL Condition (Courant Number)
Explicit method: CFL ≤ 1 is the stability condition. Implicit method: Stable even for CFL > 1, but affects accuracy and iteration count. LES: CFL ≈ 1 is recommended. Physical meaning: Information should not travel more than one cell per time step.
Residual Monitoring
Convergence is judged when residuals for Continuity Equation, momentum, and energy drop by 3–4 orders of magnitude. The mass conservation residual is particularly important.
Relaxation Factor
Pressure: 0.2–0.3, Velocity: 0.5–0.7 are typical initial values. If diverging, lower the relaxation factor. After convergence, increase to accelerate.
Internal Iterations for Unsteady Calculations
Iterate within each time step until the steady solution converges. Internal iteration count: 5–20 iterations is a guideline. If residuals fluctuate between time steps, review the time step size.
Analogy for the SIMPLE Method
The SIMPLE method is an "alternating adjustment" technique. First, velocity is tentatively determined (predictor step), then pressure is corrected so that mass conservation is satisfied with that velocity (corrector step), and velocity is revised using the corrected pressure—this back-and-forth is repeated to approach the correct solution. It resembles two people leveling a shelf: one adjusts the height, the other balances it, and they repeat this alternately.
Analogy for Upwind Differencing
Upwind differencing is a method that "stands in the river flow and prioritizes upstream information." A person in the river looking downstream cannot tell where the water comes from—it's a discretization method reflecting the physics that upstream information determines downstream. Although first-order accurate, it is highly stable because it correctly captures flow direction.
Practical Guide
P-Q Characteristic Calculation Procedure
Please tell me the procedure for obtaining a fan performance curve with CFD.
1. Baseline Calculation: Converge a steady MRF calculation at the design point flow rate.
2. Vary Flow Rate: Calculate 5–8 operating points by specifying mass flow rate (or static pressure) at the outlet.
3. Record at Each Operating Point: Total pressure rise, static pressure rise, shaft power, efficiency.
4. Efficiency Calculation: $\eta = \frac{Q \cdot \Delta p_t}{\tau \cdot \omega}$ ($\tau$: Torque, $\omega$: Angular velocity)
Related Topics
なった
詳しく
報告