Impinging Jet Heat Transfer

An impinging jet (jet impingement) is a flow where a jet ejected from a nozzle collides with a wall surface, achieving a very high heat transfer coefficient near the stagnation point. It can achieve heat transfer rates 2 to 3 times higher than typical forced convection in pipes, making it widely used in applications such as internal cooling of gas turbine blades, steel plate quenching, and electronic component cooling.

The flow is divided into three regions. (1) Free jet region: The area from the nozzle towards the wall, containing a potential core. (2) Impingement zone: The region near the wall where the flow changes direction. (3) Wall jet region: The area where the flow spreads radially along the wall.

Yes. Martin's (1977) correlation is widely used. The stagnation point Nusselt number for a single circular nozzle is

where $Re_D = u_j D / \nu$ is the Reynolds number based on nozzle diameter $D$ and jet exit velocity $u_j$. A more general form including the effect of nozzle-to-wall distance $H$ is

Many experimental results show the stagnation point Nu number is maximum at $H/D \approx 6$ to $8$.

Beyond the potential core length (typically 4 to 6D), the jet diffuses and the velocity at impingement decreases, reducing the Nu number. Conversely, for $H/D < 4$, in a confined geometry, cross-flow effects (where spent flow interferes with fresh jets) can also cause performance degradation.

Correct. In array impingement, the interference between jets and the influence of cross-flow become important. A smaller hole spacing $S/D$ increases the area-averaged Nu number, but also strengthens cross-flow, degrading the cooling performance of downstream jets. Typically, designs use $S/D = 4$ to $8$. The correlation by Florschuetz et al. (1981) is the standard reference data for array jets.

That's correct. Impinging jets are famous as a benchmark problem for turbulence models, with many models overpredicting the Nu number in the impingement zone. The main cause is the overestimation of turbulent kinetic energy production terms in the impingement region.

Specifically, the standard k-ε model can overpredict the stagnation point Nu number by more than double the experimental value. The v2f model and SST k-ω show significant improvement, but a 20-30% overprediction can still remain. Models based on the $\omega$-equation generally perform better than k-ε based ones.

According to literature reviews, the v2f model (Fluent: $\overline{v^2}$-$f$ model) tends to produce predictions closest to experimental values for impinging jets. Next is SST k-ω. However, v2f is available in Fluent and OpenFOAM (v2f turbulence model) but is not standard in STAR-CCM+.

In the impingement zone, ensure $y^+ < 1$ in the wall-normal direction, and a resolution of $\Delta r / D \approx 0.02$ to $0.05$ relative to nozzle diameter $D$ is needed in the wall-parallel direction. Sufficient cells must also be placed between the nozzle exit and the wall to resolve jet development. A typical 2D axisymmetric calculation requires 50,000 to 200,000 cells, while a 3D array jet may require millions of cells.

For a single circular nozzle, an axisymmetric (Axisymmetric) model is very efficient. Both Fluent and STAR-CCM+ have axisymmetric solvers. However, for rectangular nozzles or cases with cross-flow, 3D is mandatory.

It is actively used at the research level. Kelvin-Helmholtz instabilities generated in the jet shear layer and large-scale vortex structures in the impingement region cause unsteady fluctuations in the Nu number. LES can directly resolve these vortex structures, so the time-averaged Nu number distribution is closer to experiments than RANS. DES (Detached Eddy Simulation) and SBES are also useful as intermediate options.

For high-density data centers and next-generation power semiconductors, liquid microjets are being considered to surpass air-cooling limits. Research is advancing on arrays of 0.5mm diameter nozzles directly impinging on chip surfaces, achieving $Nu \sim 100$ to $500$.