# EN 15026 Benchmark Test Report

### 1. Purpose

This report documents the results of running the EN 15026 benchmark test against \[Software Name]. The benchmark verifies that the software correctly simulates coupled heat and moisture transport in a semi-infinite homogeneous specimen subjected to a step change in boundary conditions. Pass criteria: simulated temperature and moisture profiles at 7, 30, and 365 days must not deviate from the EN 15026 analytical reference solution by more than 2.5%.

***

### 2. Test Scenario Summary

The benchmark simulates a specimen initially in equilibrium with a constant climate, then exposed to a sudden step change:

| Parameter         | Initial Condition | Boundary Condition (t > 0) |
| ----------------- | ----------------- | -------------------------- |
| Temperature       | 20°C              | 30°C                       |
| Relative Humidity | 50%               | 95%                        |

The specimen is treated as semi-infinite and homogeneous. No surface transfer resistances are applied at the exposed (left) surface. The right surface is assumed at infinite distance from the boundary. Profiles are evaluated at **t = 7 days**, **t = 30 days**, and **t = 365 days**.

***

### 3. Material Properties Used

This section records how the EN 15026 benchmark material was defined within \[Software Name]. Note any conversions or approximations required to express the standard's analytical functions in the format the software accepts.

#### 3.1 Basic Properties

| Property                         | EN 15026 Specification | Value Entered | Notes                        |
| -------------------------------- | ---------------------- | ------------- | ---------------------------- |
| Volumetric heat capacity (ρ₀·c₀) | 1.824 × 10⁶ J/m³K      |               |                              |
| Bulk density (ρ₀)                | Derived                | kg/m³         | Arbitrary factoring of ρ₀·c₀ |
| Specific heat capacity (c₀)      | Derived                | J/(kg·K)      |                              |
| Porosity                         | 0.146                  |               | Based on u\_f = 146 kg/m³    |

#### 3.2 Thermal Conductivity

Thermal conductivity varies linearly with water content: λ = 1.5 + (15.8/1000)·w

| Water Content (kg/m³) | λ (W/mK) | Notes |
| --------------------- | -------- | ----- |
| 0                     | 1.5      |       |
| 146                   | 3.8068   |       |

**Interpolation method used:** \[Linear / Other — specify if other]

**Conversion notes:** \[Describe any adjustments needed for software input format]

#### 3.3 Moisture Storage Function

The EN 15026 moisture storage function (as a function of relative humidity at T = 293.15 K):

$$w = \frac{146}{\left(1 + \left(-8 \cdot 10^{-8} \cdot R\_{H\_2O} \cdot T \cdot \rho\_w \cdot \ln(\varphi)\right)^{1.6}\right)^{0.375}}$$

| RH (–)   | w (kg/m³) | RH (–)   | w (kg/m³) |
| -------- | --------- | -------- | --------- |
| \[value] | \[value]  | \[value] | \[value]  |
|          |           |          |           |

*(Reproduce the tabulation used as software input. Sufficient points must be included to keep tabulation error below an acceptable threshold, particularly in the 50–95% RH range relevant to this benchmark.)*

**Maximum tabulation error (full range):** \[value] kg/m³ **Maximum tabulation error (50–95% RH):** \[value] kg/m³

#### 3.4 Vapour Diffusion Resistance Factor (µ)

The EN 15026 standard specifies δ\_p directly. Conversion to µ was performed using representative conditions of ϑ = 25°C and P = 101,325 Pa:

$$\mu = \frac{1.968 \cdot 10^{-7} \cdot (25 + 273)^{0.81}}{101325 \cdot \delta\_p}$$

Tabulation was limited to the 0–95% RH range (µ → ∞ at free saturation; humidities above 95% do not occur in this benchmark).

| RH (–)   | µ (–)    | RH (–)   | µ (–)    |
| -------- | -------- | -------- | -------- |
| \[value] | \[value] | \[value] | \[value] |
|          |          |          |          |

**Maximum relative tabulation error (0–95% RH):** \[value] %

**Conversion notes:** \[Describe how the software handles δ vs. µ vs. δ\_p, and any residual discrepancy between the software's internal δ\_p evaluation and the standard's specification]

#### 3.5 Liquid Transport Coefficient (D\_w)

The EN 15026 liquid conductivity K(w) was converted to D\_w via:

$$D\_w = -K \cdot \frac{\partial p\_{suc}}{\partial w}$$

If the software applies a viscosity correction factor (temperature-dependent liquid transport), the input values must be pre-divided by the correction factor applicable at the dominant transport temperature. For this benchmark, the dominant temperature is 30°C.

| Correction applied                            | \[Yes / No]               |
| --------------------------------------------- | ------------------------- |
| Viscosity correction factor at 30°C           | \[value, expected \~1.26] |
| Input values pre-divided by correction factor | \[Yes / No]               |

Tabulation was limited to the moisture range 40–130 kg/m³ (corresponding to 50–95% RH).

| w (kg/m³) | D\_w (m²/s) | w (kg/m³) | D\_w (m²/s) |
| --------- | ----------- | --------- | ----------- |
| \[value]  | \[value]    | \[value]  | \[value]    |
|           |             |           |             |

**Maximum relative tabulation error of log(D\_w) (40–130 kg/m³):** \[value] %

***

### 4. Model Configuration

#### 4.1 Initial Conditions

| Parameter                           | Value |
| ----------------------------------- | ----- |
| Initial temperature (uniform)       | 20°C  |
| Initial relative humidity (uniform) | 50%   |

#### 4.2 Boundary Conditions

| Surface           | Heat Transfer Resistance | Vapour Resistance (s\_d) | T (°C) | RH (%) |
| ----------------- | ------------------------ | ------------------------ | ------ | ------ |
| Left (exposed)    | 0 m²K/W                  | 0 m                      | 30     | 95     |
| Right (far field) | \[high value]            | \[high value]            | —      | —      |

Boundary conditions are constant throughout the calculation period (step change applied at t = 0).

#### 4.3 Geometry and Numerical Grid

| Parameter                                    | Value          | Notes                                                   |
| -------------------------------------------- | -------------- | ------------------------------------------------------- |
| Component thickness                          | \[value] m     | Must be sufficient that right surface is unaffected     |
| Temperature rise at right surface (365 days) | \[value] °C    | Should be negligible                                    |
| Moisture penetration depth (365 days)        | \[value] m     | Expected \~0.2 m                                        |
| Total grid elements                          | \[value]       |                                                         |
| Grid refinement strategy                     | \[description] | Fine grid near exposed surface; coarse toward far field |

*(Describe sub-grid regions, element counts, and expansion factors if applicable.)*

#### 4.4 Calculation Period

| Parameter            | Value                                         |
| -------------------- | --------------------------------------------- |
| Start date           | \[DD.MM.YYYY]                                 |
| End date             | \[DD.MM.YYYY] (at least 365 days after start) |
| Profile output dates | Day 7, Day 30, Day 365                        |
| Time step            | \[value] h                                    |

***

### 5. Results

#### 5.1 Moisture Profiles

Comparison of simulated water content w(x) against EN 15026 analytical reference at t = 7, 30, and 365 days.

**\[Insert Figure: Moisture distribution at 7, 30, and 365 days. Plot both simulated and reference curves. Include the ±2.5% permissible error band.]**

| Time     | Max. deviation from reference | Pass / Fail |
| -------- | ----------------------------- | ----------- |
| 7 days   | \[value] %                    |             |
| 30 days  | \[value] %                    |             |
| 365 days | \[value] %                    |             |

#### 5.2 Temperature Profiles

Comparison of simulated temperature T(x) against EN 15026 analytical reference at t = 7, 30, and 365 days.

**\[Insert Figure: Temperature distribution at 7, 30, and 365 days. Plot both simulated and reference curves. Include the ±2.5% permissible error band.]**

| Time     | Max. deviation from reference | Pass / Fail |
| -------- | ----------------------------- | ----------- |
| 7 days   | \[value] %                    |             |
| 30 days  | \[value] %                    |             |
| 365 days | \[value] %                    |             |

***

### 6. Deviations and Known Limitations

*This section documents any systematic differences between the software's internal transport model and the exact formulation used by EN 15026. These are not errors; they are model characteristics that affect how the benchmark material properties must be prepared.*

| Issue                                      | EN 15026 Assumption                  | Software Behaviour                      | Workaround Applied                         |
| ------------------------------------------ | ------------------------------------ | --------------------------------------- | ------------------------------------------ |
| Temperature dependence of liquid transport | Temperature-independent K(w)         | Automatic viscosity correction applied  | Pre-divide D\_w by correction factor       |
| δ\_p formulation                           | Explicit δ\_p(w) function            | Internal µ-based model, auto-computes δ | Convert δ\_p → µ at representative T and P |
| Moisture storage function                  | Temperature-dependent (T in formula) | Temperature-independent                 | Use reference T = 293.15 K as fixed value  |
| \[Other software-specific issue]           | \[Standard assumption]               | \[Software behaviour]                   | \[Action taken]                            |

***

### 7. Overall Compliance

| Criterion                                         | Result         |
| ------------------------------------------------- | -------------- |
| All moisture profiles within 2.5% of reference    | \[Pass / Fail] |
| All temperature profiles within 2.5% of reference | \[Pass / Fail] |
| General requirements of EN 15026 met              | \[Pass / Fail] |

**Overall verdict:** \[PASS / FAIL]

***

### 8. Notes and Observations

*Use this section for anything worth flagging: numerical instabilities observed during testing, sensitivity to grid refinement, tabulation resolution effects, or anything that required more than one attempt to get right (there's usually something).*

\[Free text]

***

### 9. Document Control

**Revision History:**

| Version | Date  | Author | Changes         |
| ------- | ----- | ------ | --------------- |
| 1.0     | xxxxx | DOD    | Initial release |

***

### Appendix A: Material Property Tables (Full Tabulations)

*Reproduce the complete input tables used for moisture storage function, µ-value, and D\_w as submitted to the software.*

#### A.1 Moisture Storage Function Table

| RH (–) | w (kg/m³) |
| ------ | --------- |
|        |           |

#### A.2 µ-Value Table

| RH (–) | µ (–) |
| ------ | ----- |
|        |       |

#### A.3 Liquid Transport Coefficient Table

| w (kg/m³) | D\_w (m²/s) |
| --------- | ----------- |
|           |             |


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