HVAC空調CFD
Theory and Physics
Overview
Teacher! In what situations is CFD analysis used for HVAC air conditioning?
It's a technology that uses CFD to predict airflow distribution, temperature distribution, ventilation efficiency, and comfort (PMV/PPD) for indoor environments such as offices, commercial facilities, data centers, and hospitals. It is widely used from performance verification in the design stage of air conditioning equipment to renovation plans for existing buildings.
Governing Equations
Please tell me the governing equations for indoor airflow.
The basics are the incompressible Navier-Stokes equations + energy equation for low-speed flow (Mach number < 0.3). Buoyancy effects are incorporated using the Boussinesq approximation.
This term is added as a source term to the Navier-Stokes equations. $\beta$ is the volumetric expansion coefficient (for air, $\beta \approx 1/T_0$ [1/K]).
The Boussinesq approximation is for small temperature differences, right? For indoor air conditioning, up to what temperature difference is it acceptable?
The condition is $\beta \Delta T \ll 1$, so for air, it's reasonable for $\Delta T < 30$ K or so. For indoor air conditioning, it's usually within 10 K, so it's not a problem.
Comfort Indicators
How is PMV (Predicted Mean Vote) calculated in CFD?
PMV is a thermal comfort indicator defined in ISO 7730, calculated from six parameters.
| Parameter | Symbol | How to obtain from CFD |
|---|---|---|
| Metabolic rate | M | Set from activity level (office work: 1.2 met) |
| Clothing insulation | I_cl | Set from season/use (summer clothing: 0.5 clo) |
| Air temperature | T_a | Directly obtained from CFD results |
| Mean radiant temperature | T_r | Calculated from CFD + radiation model |
| Air velocity | v_a | Directly obtained from CFD results |
| Relative humidity | RH | Calculated via Species Transport, or assumed uniform |
If mean radiant temperature is needed, then the radiation model must also be turned ON, right?
Correct. Use the S2S (Surface-to-Surface) model or DO (Discrete Ordinates) model to calculate radiative heat transfer between wall surfaces and determine T_r at each point.
Ventilation Efficiency Evaluation Indicators
What kind of indicators are there for ventilation efficiency?
Here is a summary of typical indicators.
| Indicator | Definition | Meaning |
|---|---|---|
| ACH (Air Changes per Hour) | Q / V_room | Air change rate |
| AE (Air Exchange Efficiency) | τ_n / (2τ_mean) | Fresh air distribution efficiency |
| SVE (Contaminant Removal Effectiveness) | C_e / C_mean | Pollutant removal efficiency |
| Local Mean Age of Air | τ(x) | Air residence time at each point |
How is Local Mean Age of Air calculated in CFD?
Add a scalar transport equation to calculate the mean residence time of air. In Fluent, use UDS (User Defined Scalar).
Since the source term is $\rho$ (uniform), $\tau$ becomes larger the longer air stays in the room, right?
The Origin of HVAC CFD—Indoor Airflow Analysis Born from 1970s Building Energy Issues
CFD analysis of indoor airflow (Room CFD) became full-fledged after the 1970s oil crisis, when the need for energy-efficient building design increased. Initially, simple mixed-air models called Zone Models were mainstream, but with the spread of computers, Navier-Stokes solvers began to be applied to indoor airflow. Nielsen (1974) first published k-ε model analysis of indoor airflow, providing a scientific basis for supply/return outlet design. This was the starting point for modern CFD-HVAC analysis. 40 years later, unsteady LES analysis with millions of cells has become standard, enabling real-time prediction of ventilation efficiency and occupant thermal comfort (PMV indicator).
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 unstable and splashing, but after a while, the flow becomes steady, 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/closes—all are unsteady phenomena. So what is steady-state analysis? Looking only at "after sufficient time has passed and the flow has settled"—meaning setting this term to zero. This significantly reduces computational cost, so 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 side of a room is also because the "carrier," air, 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" → They are completely different! Convection is carried by flow, conduction is transmitted by molecules. There's 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 a syringe plunger, 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 provides the force pushing the fluid. Dam water release 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 common misunderstanding here: "Pressure" in CFD is often gauge pressure, not absolute pressure. When switching to compressible analysis, if results become strange, it might be due to confusion between absolute/gauge pressure.
- Source term $S_\phi$: Warmed 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 source terms. What happens if you forget a source term? In natural convection analysis, forgetting buoyancy means the fluid doesn't move at all—a physically impossible result where warm air doesn't rise in a winter room with the heater on.
Assumptions and Applicability Limits
- Continuum assumption: Valid for Knudsen number Kn < 0.01 (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 or above, consider compressibility effects
- Boussinesq approximation (Natural convection): Consider density variation 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 coefficient $\nu = \mu/\rho$ [m²/s] |
| Reynolds number $Re$ | Dimensionless | $Re = \rho u L / \mu$. Indicator for laminar/turbulent transition |
| CFL number | Dimensionless | $CFL = u \Delta t / \Delta x$. Directly related to time step stability |
Numerical Methods and Implementation
Details of Numerical Methods
Please tell me the specific implementation for HVAC CFD.
Turbulence Model Selection
For indoor airflow, SST k-omega or RNG k-epsilon is recommended. Especially for ceiling-supply mixing ventilation, SST k-omega is preferred because wall jet behavior is important.
| Ventilation Method | Recommended Turbulence Model | Reason |
|---|---|---|
| Mixing ventilation (ceiling supply) | SST k-omega | Captures wall jet separation |
| Displacement ventilation (floor supply) | RNG k-epsilon | Handling of laminar-turbulent transition region |
| Personal ventilation | SST k-omega | Accuracy for low-velocity jets |
| Natural ventilation | SST k-omega + Boussinesq | Compatible with buoyancy-driven flow |
Supply Outlet Modeling
Air conditioning supply outlets have complex shapes, right? Do you mesh them all?
Meshing the entire internal shape of a diffuser is inefficient. Instead, use the Simplified Diffuser Model (SDM). It's a method of directly applying a velocity profile (wind speed, angle, turbulence quantities) to the supply outlet surface.
Common settings by diffuser type:
| Diffuser | Supply Angle | Effective Area Ratio | Turbulence Intensity |
|---|---|---|---|
| 4-way ceiling cassette | Horizontal ~ 15° down | 50–70% | 10–15% |
| Anemostat | Radial, 45° | 60–80% | 15–20% |
| Linear diffuser | Horizontal | 70–90% | 10% |
| Pan louver | Variable (0–60°) | 80–95% | 5–10% |
| Floor supply outlet | Vertical upward | 20–40% | 20–30% |
What is the effective area ratio?
It's the ratio of the effective supply area to the diffuser neck area. It's the area excluding parts shadowed by louvers or fins. Verify CFD validity by cross-referencing with the Coanda effect reach distance listed in manufacturer catalogs.
Mesh Strategy
What is a guideline for mesh count in indoor spaces?
For a typical office (10m x 15m x 3m), 2 million to 10 million cells is a guideline.
| Region | Cell Size |
|---|---|
| Supply/Return outlet vicinity | 10–30 mm |
| Human body / furniture vicinity | 20–50 mm |
| Occupied zone (FL+0.1m ~ FL+1.8m) | 30–80 mm |
| Ceiling vicinity (jet region) | 20–50 mm |
| Other (space center) | 80–200 mm |
Radiation Model Settings
Which radiation model should I use?
For indoor environments, the S2S (Surface-to-Surface) model is recommended. It pre-calculates View Factors between wall surfaces to evaluate radiative heat transfer. The DO model can also be used, but for indoor environments with only opaque walls, S2S is sufficient.
Wall surface emissivity settings:
| Surface | Emissivity |
|---|---|
| Concrete wall | 0.90–0.95 |
| Glass window | 0.84–0.90 |
| Metal (painted) | 0.85–0.95 |
| Metal (unpainted) | 0.05–0.20 |
| Human body surface | 0.95–0.97 |
How is solar radiation through glass windows handled?
Enable the Solar Load Model to calculate solar heat gain from the sun's position (latitude, longitude, date, time) and the window's SHGC (Solar Heat Gain Coefficient). This feature is standard in Fluent.
Turbulence Model Selection for HVAC CFD—Limitations of Standard k-ε in Low Reynolds Number Environments
CFD analysis for indoor airflow (HVAC) is a special environment that is lower speed (Re=10³–10⁵) and more influenced by buoyancy than external fluid analysis. The standard k-ε model tends to overestimate buoyancy-driven flow in this low Reynolds number region, reducing prediction accuracy for thermal stratification. More appropriate choices are ① RNG k-ε (well-balanced) ② Low-Re k-ε model (Launder-Sharma, etc.) ③ LES (highest accuracy, high cost). According to verification reports from the Architectural Institute of Japan, for natural convection-dominated regions with supply velocities below 0.5m/s, RNG k-ε matches LES results within 10%.
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