Gnielinski相関式

Roughly speaking, that's correct. The Gnielinski correlation can be used over a very wide range of Re = 2,300 to 5×10⁶, and it also covers the transition region (around Re = 2,300 to 10,000). The Dittus-Boelter correlation only assumes fully turbulent flow with Re > 10,000, so it cannot be used in the transition region.

The Gnielinski correlation has an accuracy of ±10% against experimental data. In contrast, the Dittus-Boelter correlation has an accuracy of ±25%. That means it's more than twice as accurate. Therefore, in current textbooks and design standards, the Gnielinski correlation is recommended unless there is a specific reason not to use it. It is also often used as a benchmark for CFD wall function validation.

No, the Dittus-Boelter correlation is still useful for rough estimates and hand calculation cross-checks because of its simple form. However, using the Gnielinski correlation for final design values is the standard practice in the field.

Good question. There's a historical flow. First, in 1970, Petukhov proposed a turbulent heat transfer model based on the analogy between momentum and heat transport. However, the Petukhov correlation was limited to fully turbulent flow with Re > 10⁴.

In 1976, Gnielinski modified the Petukhov correlation by introducing a key revision: replacing the Re term with (Re − 1000). This single modification allowed accurate prediction even in the transition region. It's a simple but physically profound modification that effectively captures the phenomenon that "the effective Re is smaller in regions where turbulence is not fully developed."

Yes, excellent engineering models are often simple. Gnielinski himself, at the Karlsruhe Institute of Technology in Germany, compared and validated this modification against a vast amount of experimental data, showing it maintains high accuracy over the widest range. Now it's a standard to the point where "for internal flow turbulent heat transfer, it's the Gnielinski correlation."

The Gnielinski correlation is as follows:

Here, $\mathrm{Nu}$ is the Nusselt number, $\mathrm{Re}$ is the Reynolds number, $\mathrm{Pr}$ is the Prandtl number, and $f$ is the Darcy friction factor.

This term represents the thermal resistance of the viscous sublayer. Very close to the wall, there is a thin layer dominated by viscosity (the viscous sublayer), where turbulent mixing is almost ineffective. The influence of this layer becomes larger for fluids whose Pr deviates significantly from 1. For example, in oil (Pr ≈ 100–1000), the thermal resistance of the viscous sublayer is quite large, and Nu is lower compared to water (Pr ≈ 7). Conversely, for gases (Pr ≈ 0.7), the viscous sublayer is thin, so the effect is small.

Exactly. The Dittus-Boelter correlation only approximates Pr with a power law, but the Gnielinski correlation models the thermal resistance of the viscous sublayer and the turbulent core separately. That's why its accuracy is significantly better, especially for fluids where Pr is far from 1 (oil, high-viscosity refrigerants, etc.).

The one to use together with the Gnielinski correlation is the Petukhov friction factor:

This gives the Darcy friction factor for turbulent flow in smooth circular pipes and closely matches the smooth pipe curve on the Moody chart. It is valid for Re = 3,000 to 5×10⁶.

Yes. However, for rough pipes (relative roughness ε/D > 0), you cannot use the Petukhov equation as is. For rough pipes, you would determine $f$ from the Colebrook-White equation or the Churchill equation and then plug it into the Gnielinski correlation. However, it's important to understand that in that case, it is "outside the guaranteed accuracy range of the Gnielinski correlation."

No, there are clear applicability conditions. Accuracy is not guaranteed outside these:

Correct. For liquid metals, the viscous sublayer is almost non-existent, so heat conduction becomes dominant even into the bulk flow. The viscous sublayer model in the denominator of the Gnielinski correlation doesn't hold. For liquid metals, use the Lyon-Martinelli correlation or the Seban-Shimazaki correlation. Conversely, for very high viscosity fluids (Pr > 2,000), models with wall temperature corrections like the Sieder-Tate correlation are often more reliable.

Let's compare for a case of water flowing in a circular pipe. Conditions: D = 25 mm, T_bulk = 50°C (Pr ≈ 3.56).

The Dittus-Boelter correlation tends to overestimate Nu as Re increases. This might seem like a conservative (safe) estimate, but in cooling system design, it can be dangerous by leading to the misconception that "the actual cooling performance is higher than expected."

Exactly. Especially for oil (Pr ≈ 100 or more), the difference widens further. That's because the Pr^0.4 approximation in the Dittus-Boelter correlation becomes crude. Even in equipment manufacturers' design standards and heat exchanger design tools like HTRI or ASPEN, the Gnielinski correlation is the default.

Good point. CFD solvers directly solve the Navier-Stokes equations, so empirical correlations like Gnielinski's are not used in the "internal calculations of the solver." The role of the Gnielinski correlation is in verification and validation. Specifically, it's used like this:

• Validation of Wall Function Appropriateness: Compare the wall heat transfer coefficient $h$ or Nu number obtained from CFD with the analytical solution from the Gnielinski correlation. If the discrepancy is more than 20%, review the y+ setting or mesh resolution.
• Mesh Convergence Confirmation: Confirm that as the mesh is progressively refined, the CFD Nu converges to the value from the Gnielinski correlation.
• Turbulence Model Selection: Compare Nu prediction values from different models (k-ε, k-ω SST, RSM, etc.) with the Gnielinski correlation to select the model suitable for the problem at hand.

It's very important. When using the wall function approach (y+ = 30–300), if the Nu from CFD matches the Gnielinski correlation Nu within ±10%, it can be judged that the wall function is working appropriately. For wall-resolved (Low-Re) meshes (y+ < 1), it should almost perfectly match the Gnielinski correlation. If it doesn't match, there is likely a problem with the turbulence model or boundary conditions.

Actually, its most common use in practical work is in 1D system-level analysis. For example:

• Heat Exchanger Design: HTRI Xchanger Suite, ASPEN Exchanger Design & Rating use the Gnielinski correlation as the default for calculating the tube-side heat transfer coefficient.
• Piping System Thermal Analysis: Standard model for calculating h for internal forced convection in 1D thermal-hydraulic codes like Flownex or FLOWMASTER.
• Nuclear Safety Analysis: Gnielinski-based models are used in nuclear reactor thermal-hydraulic codes like RELAP5 or TRACE.
• Automotive Cooling Systems: Predicting heat transfer for coolant (water + ethylene glycol mixture) inside engine cooling jackets.

In the Gnielinski correlation, properties are evaluated at the bulk mean temperature $T_b$ (cross-sectional average fluid temperature) as a principle. However, for cases with a large temperature difference between the wall and the fluid, the Sieder-Tate viscosity correction is added:

Here, $\mu_b$ is the viscosity at the bulk temperature, and $\mu_w$ is the viscosity at the wall temperature. For heating, $\mu_b > \mu_w$, so Nu increases; for cooling, Nu decreases. This correction becomes significant especially for oil-based fluids when the wall-fluid temperature difference exceeds 50°C.