ASHRAE Standards and CAE Thermal Fluid Simulation

Category: 熱解析 > 建築設備 | Integrated 2026-04-12
ASHRAE thermal comfort PMV distribution and CFD airflow simulation in office space
ASHRAE規格に基づく室内熱環境のCFD解析 ── 空調吹出し口からの気流パターンとPMV分布の可視化

Theory and Physics

Overview of ASHRAE Standards

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Professor, how are ASHRAE standards related to CAE? I only have an image of them as building codes...

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Simply put, ASHRAE is the American Society of Heating, Refrigerating and Air-Conditioning Engineers, an organization that sets the "pass/fail criteria" for HVAC design. Its relationship with CAE is direct. For example, ASHRAE 55 is the standard for indoor thermal comfort, and CFD is used to analyze airflow patterns and temperature distributions from air conditioning diffusers to verify compliance with that standard. ASHRAE 90.1 is the energy efficiency standard, requiring compliance verification through building energy simulation.

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What? CFD results are used to determine pass/fail against building codes?

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That's right. Especially in data center cooling design, ASHRAE TC9.9 defines environmental classes, and for Class A1, whether the intake temperature meets 18–27°C becomes the pass/fail criterion in CFD. Since verification by actual measurement alone is impossible before construction, CFD plays the role of "ASHRAE compliance verification at the design stage."

ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers), founded in 1894, is an international authority in the HVAC field, and its suite of standards functions as the "pass/fail criteria" for CAE analysis. The main standards covered in this article are as follows.

StandardTargetApplication in CAE
ASHRAE 55Indoor Thermal ComfortAnalyze air temperature, wind speed, radiant temperature with CFD for PMV/PPD judgment
ASHRAE 62.1Ventilation and Indoor Air QualityEvaluate CO2 concentration distribution and ventilation efficiency (air age) with CFD
ASHRAE 90.1Building Energy EfficiencyCalculate energy consumption with EnergyPlus etc. and compare with baseline values
ASHRAE TC9.9Data Center EnvironmentPredict temperature distribution between server racks and hot spots with CFD
ASHRAE 170Healthcare Facility VentilationAnalyze airflow patterns and contaminant dispersion in operating rooms with CFD

ASHRAE 55 and Thermal Comfort Model (PMV/PPD)

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I often hear about ASHRAE 55, but what exactly does it judge?

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ASHRAE 55 is a standard that numerically judges "whether people in a room feel thermally comfortable, neither too hot nor too cold." Its core is the PMV (Predicted Mean Vote) model proposed by Professor Fanger (Technical University of Denmark), based on the human body's heat balance equation.

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Human body heat balance, is that about thermoregulation?

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Exactly. The metabolic heat $M$ minus the work $W$ is dissipated from the body to the environment. The dissipation paths are convection, radiation, and evaporation. If these are balanced, it's comfortable (PMV = 0). If heat cannot be dissipated sufficiently, it's hot (PMV > 0). If dissipation is excessive, it's cold (PMV < 0). In equation form, it looks like this:

$$ \text{PMV} = f(M, W, I_{cl}, f_{cl}, t_a, \bar{t}_r, v_a, p_a) $$

Here, each variable is as follows:

VariableMeaningTypical Value (Office)
$M$Metabolic rate [W/m²]58.2 (1.0 met, seated light work)
$W$External work rate [W/m²]0 (usually negligible)
$I_{cl}$Clothing insulation [clo]0.5 (summer) ~1.0 (winter)
$f_{cl}$Clothing area factor [-]$1.00 + 1.290 \, I_{cl}$ (if $I_{cl} \leq 0.078$)
$t_a$Air temperature [°C]23–26
$\bar{t}_r$Mean radiant temperature [°C]Calculated from wall/window surface temperatures
$v_a$Air velocity [m/s]0.1–0.2
$p_a$Water vapor partial pressure [Pa]Equivalent to 40–60% relative humidity
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What is the passing criterion for ASHRAE 55?

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Compliance is achieved if PMV falls within the range $-0.5 \leq \text{PMV} \leq +0.5$. This corresponds to a PPD (Predicted Percentage Dissatisfied) of 10% or less. The PPD calculation formula is:

$$ \text{PPD} = 100 - 95 \cdot \exp\left(-0.03353 \cdot \text{PMV}^4 - 0.2179 \cdot \text{PMV}^2\right) $$
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So, if we calculate PMV throughout the room with CFD and all occupied zones fall within -0.5 to +0.5, it passes, right?

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That's correct. However, be careful: what CFD provides is only air temperature $t_a$ and air velocity $v_a$. Calculating PMV also requires radiant temperature $\bar{t}_r$ and humidity $p_a$. The former requires view factor calculations or radiation models, and the latter requires solving the moisture transport equation. Therefore, ASHRAE 55 compliance assessment is essentially a multiphysics problem.

Complete Heat Balance Equation for PMV

The thermal load on the human body $L$ used in PMV calculation is defined as follows:

$$ L = (M - W) - 3.05 \times 10^{-3}(5733 - 6.99(M-W) - p_a) $$
$$ - 0.42\bigl((M-W) - 58.15\bigr) - 1.7 \times 10^{-5} M(5867 - p_a) $$
$$ - 0.0014\,M(34 - t_a) - 3.96 \times 10^{-8} f_{cl}\bigl((t_{cl}+273)^4 - (\bar{t}_r+273)^4\bigr) $$
$$ - f_{cl} \, h_c (t_{cl} - t_a) $$

Here, $t_{cl}$ is the clothing surface temperature (obtained by iterative calculation), $h_c$ is the convective heat transfer coefficient ($h_c = \max(2.38|t_{cl}-t_a|^{0.25},\; 12.1\sqrt{v_a})$). PMV is calculated using this $L$ as $\text{PMV} = (0.303 \, e^{-0.036M} + 0.028) \cdot L$.

ASHRAE 62.1 and Ventilation Analysis

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ASHRAE 62.1 is the ventilation standard, right? Is this also verified with CFD?

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Yes. ASHRAE 62.1 specifies the minimum required outdoor air rate for each use. For example, for offices, it's 2.5 L/s per person + 0.3 L/s/(m²) per floor area. However, just "bringing in air" is not enough; it's crucial that it reaches all occupied zones. In large spaces or offices with complex partitions, simple airflow calculations can overlook short-circuiting (where supplied air is immediately drawn into the exhaust).

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Short-circuiting seems very wasteful. How is that detected with CFD?

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A commonly used metric in practice is Air Age (Local Mean Age of Air). This is the average time air has spent in the room before reaching a certain point. In CFD, it is obtained by adding a scalar transport equation:

$$ \frac{\partial (\rho \tau)}{\partial t} + \nabla \cdot (\rho \mathbf{u} \tau) = \nabla \cdot \left(\frac{\mu_{\text{eff}}}{\text{Sc}_t} \nabla \tau\right) + \rho $$

Here, $\tau$ is the air age [s], $\mu_{\text{eff}}$ is the effective viscosity (laminar + turbulent), $\text{Sc}_t$ is the turbulent Schmidt number (typically 0.7–0.9), and the $\rho$ on the right side is the source term representing "passage of time." By solving with $\tau = 0$ (fresh air) at the supply inlet, the air age distribution at each point in the room is obtained.

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So, areas with high air age = poorly ventilated areas. Are there any judgment criteria?

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ASHRAE 62.1 uses an indicator called Ventilation Effectiveness $E_v$. For perfect mixing, $E_v = 1.0$; for displacement ventilation, $E_v = 1.2$ is typical. It can be calculated from the air age distribution obtained by CFD as $E_v = \tau_n / (2 \langle\tau\rangle)$ ($\tau_n$: nominal time constant = room volume / ventilation rate, $\langle\tau\rangle$: average air age at the exhaust). If there are areas with $E_v < 0.8$, the position of supply outlets or the shape of diffusers needs to be reviewed.

ASHRAE 90.1 and Energy Efficiency Standards

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ASHRAE 90.1 is the energy standard, right? Is that more about energy simulation than CFD?

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Good point. ASHRAE 90.1-2022 has three compliance paths. Prescriptive is the method of keeping insulation performance and lighting density below specified values. ECB (Energy Cost Budget) compares energy costs with a reference building. And Performance Rating (PRM) is simulation based on APPENDIX G. For LEED certification, PRM is virtually mandatory, requiring calculation of annual energy consumption using dynamic energy simulation tools like EnergyPlus or eQUEST.

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So, CFD and building energy simulation are separate things?

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Basically, yes. Energy simulation calculates the annual energy balance of the entire building over time, assuming one zone = perfect mixing. CFD is a 3D analysis with spatial resolution. However, in practice, linking these two is becoming more common. For example, using the non-uniform indoor temperature distribution obtained from CFD as a correction factor in energy simulation, or using the natural ventilation airflow rate obtained from CFD as input for EnergyPlus's ventilation module.

The most important energy performance indicator in ASHRAE 90.1 is EUI (Energy Use Intensity), with units of kBtu/ft²/year or kWh/m²/year. The baseline building EUI for an office building is about 85 kBtu/ft²/year (ASHRAE 90.1-2019 baseline), and the design building must prove it is lower than this.

Data Center Cooling Classes (TC9.9)

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Data centers were mentioned earlier, but what kind of standard is ASHRAE TC9.9?

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ASHRAE TC9.9 (Technical Committee 9.9) publishes "Thermal Guidelines for Data Processing Environments," classifying IT equipment operating environments into four classes. This is the standard most frequently referenced in data center CFD design.

ClassIntake Temperature [°C]Relative Humidity [%RH]Maximum Dew Point [°C]Target Equipment
A1 (Recommended)18 – 2720 – 8017Mission-critical servers
A210 – 3520 – 8021General IT equipment
A35 – 408 – 8524Environmentally robust equipment
A45 – 458 – 9024For special applications
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A1 is the strictest. How is it checked with CFD?

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Calculate the temperature distribution at the intake face of the server racks (cold aisle side) and verify that all points fall within the A1 range of 18–27°C. A common problem is hot spots. This is a phenomenon where exhaust air (over 40°C from the hot aisle side) recirculates to the top of racks or the ends of rack rows, raising the intake temperature. This is called "bypass air" or "recirculation." CFD can detect this in advance by producing temperature maps per rack.

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I see, if CFD finds areas exceeding 27°C, then design changes are needed, right? Like adding floor blanking panels?

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Exactly. In practice, measures such as (1) optimizing perforated floor tile opening ratios and placement, (2) blanking panels (blocking empty slots), (3) cold aisle/hot aisle containment, and (4) repositioning in-row precision air conditioners (CRAC/CRAH) are parametrically studied using CFD. Quantifying the degree of recirculation using indicators like SHI (Supply Heat Index) or RHI (Return Heat Index) is also common.

Coffee Break Trivia Corner

ASHRAE History and Influence

ASHRAE was founded in 1894 as ASHE (American Society of Heating Engineers) and merged with ASREE (American Society of Refrigerating Engineers) in 1959 to become its current name. The first edition of ASHRAE Standard 55 was in 1966, and Fanger's (Technical University of Denmark) PMV theory was fully adopted in the 1992 revision. The current standard system influences building codes in over 180 countries and also forms the basis of Japan's JIS A4001. The 2023 edition of ASHRAE 55 formally adopted the Adaptive Comfort Model reflecting individual differences for naturally ventilated buildings, increasing flexibility for climate change adaptation.

Numerical Methods and Implementation

CFD Governing Equations and Turbulence Model Selection

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When verifying ASHRAE compliance with CFD, are the governing equations the usual Navier-Stokes?

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Yes. For indoor HVAC CFD, the basic equations are the incompressible RANS equations with a buoyancy term using the Boussinesq approximation:

$$ \nabla \cdot \mathbf{u} = 0 $$
$$ \rho \frac{\partial \mathbf{u}}{\partial t} + \rho (\mathbf{u} \cdot \nabla)\mathbf{u} = -\nabla p + \nabla \cdot \bigl[(\mu + \mu_t)(\nabla \mathbf{u} + \nabla \mathbf{u}^T)\bigr] - \rho_0 \beta (T - T_0) \mathbf{g} $$
$$ \rho c_p \frac{\partial T}{\partial t} + \rho c_p (\mathbf{u} \cdot \nabla)T = \nabla \cdot \left[(k + \frac{\mu_t c_p}{\text{Pr}_t})\nabla T\right] + Q $$

Here, $\beta$ is the volumetric expansion coefficient, $T_0$ is the reference temperature, $\mu_t$ is the eddy viscosity coefficient, and $\text{Pr}_t$ is the turbulent Prandtl number (typically 0.85–0.9).

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Which turbulence model is best to use? There are various ones like k-ε and SST, right?

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The choice of turbulence model for indoor HVAC CFD varies by application. I've summarized the practical usage in a table:

ModelRecommended UseAdvantagesCaveats
RNG k-εSteady-state analysis of entire officesStable, low computational costLow accuracy for swirling/separated flows
SST k-ωAirflow analysis near diffusersHigh accuracy near wallsSlightly higher computational cost than k-ε
LES (Large Eddy Simulation)Transient thermal environment evaluationResolves unsteady turbulent structuresComputational cost 10–100 times higher
Zero-equationInitial design for data centersExtremely fastAccuracy is qualitative
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Zero-equation models can be used for data centers? Isn't that a bit coarse?

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Zero-equation models are mainstream in data center-specific tools (like 6SigmaDCX, Cadence Reality DC). This prioritizes "solving large-scale models containing thousands of racks in minutes." Accuracy is around ±2°C at rack intake faces. Ideally, final design verification would recalculate with RNG k-ε or SST k-ω, but for parametric studies in early design stages like data center PUE (Power Usage Effectiveness) optimization, zero-equation is sufficient.

Numerical Methods for PMV Calculation

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When calculating PMV from CFD results, how is it done specifically?

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