Fan and Blower CFD
Fan and Blower CFD: Theoretical Foundations
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 TheoryโFrom Rankine-Froude Momentum Theory to Prandtl Wing Theory
Fan aerodynamic theory shares the same history as propeller theory, starting with the Rankine-Froude (1865โ1878) 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.
Computational Methods for Fan and Blower CFD
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/(3000ร7) = 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 CFDโMulti-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 5โ10 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 2โ3 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.
Fan and Blower CFD in Practice
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 5โ8 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)
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