# NACA submerged duct

There is a need for efficient air-induction systems as pressure losses in the air-induction system may result in a loss in power output, which is specially true for rear engined cars. The way to introduce air into a vehicle can be through a submerged duct or a duct exposed to the flow —scoop—, each with it’s pros and cons.

In this article I will focus on the former, which have enjoyed a lot of popularity over the past few decades, as shown by the Ferrari F40 in the image below.

## Simulation model

For the simulation I will try to replicate the Ames 1– by 1.5–foot wind channel, shown in the next figure, so that I can compare experimental results with simulation in a 1-to-1 basis.

The opening is of 4-square-inch area (4– by 1–inch), just ahead an 8° conical diffuser of 13 to 1 area ratio which expands the air to a very low velocity. Pressure probes are placed both at the entrance and at the end of the diffuser, as shown in the following figure. In the simulation, virtual probes are used instead of the physical probes of the experiments.

The NACA duct consists on curved divergent walls and a 7° ramp. The effect of the divergent wall is to reduce the losses suffered by the air entering the duct. Frick et al. surmise that the divergent walls of the ramp act to reduce the amount of boundary layer air which flows down the ramp.

In the present simulations we are using design 4 for the divergent ramps.

### Setup

A high quality tetrahedral mesh was chosen, cramming some 7.5M cells into a relatively small volume. This relatively high cell count is a consequence of the willingness to resolve the boundary layer, with 13 layers of prismatic cells targeting a y+ value of 1 in the first cell.

The boundary conditions are summarized in the following table.

 Boundary inlet outlet duct_outlet walls p zeroGradient fixedValueuniform 0 zeroGradient zeroGradient U fixedValueuniform (30 0 0) zeroGradient fixedValue*case dependent fixedValueuniform (0 0 0) k fixedValueuniform 0.0337 zeroGradient zeroGradient fixedValueuniform 1e-10 omega fixedValueuniform 225 zeroGradient zeroGradient fixedValueuniform 1e-10 nut calculateduniform 0 calculateduniform 0 calculateduniform 0 nutUSpaldingWallFunctionuniform 0

The values for k, omega, and nut at the walls are the recommended ones for cases where one wants to resolve the boundary layer, i.e., y+ is below 6 (Guerrero, 2016).

The highest y+ value in our simulation is 2.5 in the high velocity region at the top of the lip. The mesh could have been refined further, but as the maximum y+ value was still within the viscous sub-layer, no further action was taken.

## Results

There’s a wealth of results out of the thirteen simulations ran to cover a wide inlet-velocity ratio spectrum, from which I’ll extract the most relevant.

### Dynamic pressure recovery

In order to estimate the total pressure losses, Frick et al. (1945) used the following expression:

$$\frac{\Delta H}{q_o} = \frac{\Delta H_A}{q_o} + (1 – \eta)\left( \frac{V_A}{V_o} \right )^2\left\{ 1 – 0.2 M^2 \left[ \left( \frac{V_A}{V_o} \right)^2 – 1 \right] \right\}^{2.5}$$

where $H$ is total pressure, $q$ is dynamic pressure, $\eta$ is the diffuser efficiency, $V$ is the velocity —$A$ at the duct entrance and $o$ for free stream— and $M$ is the Mach number. The efficiency can be calculated as follows (Mossman & Randall, 1948):

$$\eta = \frac{H_D – p_A}{H_A – p_A}$$

where the subscript $D$ refers to the station after diffusion, and $A$ to the duct-entrance station.

The dynamic pressure recovery obtained for lip 6 and convergent wall 4 at different inlet-velocity ratios is shown in the following chart.

There is a noticeable difference between experiment and simulation, although the pressure recovery tends to decrease with increasing inlet-velocity ratios. It might be worth noting that Frick et al. (1945) made the measurements of the pressure recovery at the end of the diffuser while the pressure measuring rakes were located in the duct inlet. That, according to the authors, resulted in considerable pressure losses which could explain the differences between experiment and simulation.

### Total pressure

The chart shows a small dip in the dynamic pressure recovery at low inlet-velocity ratios. If we display the 0 Pa total relative pressure isosurface we can see two tubes forming at the entrance of the duct at 0.25 and 0.3 inlet-velocity ratios, which coincides with the drop in pressure recovery.

Another detail that we can observe is the propagation of pressure losses towards the interior of the diffuser as we increase the inlet velocity. We can only imagine what would have been the scenario in Frick et al.’s experiment in which they kept the pressure tubes at the inlet of the duct.

### Velocity

The tubes that we saw in the isosurfaces of total pressure are the result of the recirculation of the flow as can be seen in the following animation.

At first it might appear that this recirculation is the result of air bypassing the divergent wall to enter the duct. But the streamlines show a different scenario, and that is that these vortices are formed by the excess air that is at the entry of the duct and seeks to join back the free stream.

### Drag

It is impossible to distinguish between internal and external drag of a submerged inlet; but Frick et al. (1945) expect the external drag to be a negative quantity due to flow improvement behind the inlet as the boundary layer would have been removed. Nowadays, with the assistance of CFD, we can estimate drag individually for each surface part and get a better distinction between internal and external drag.

In the upper graph I show the evolution and distribution of the drag on the NACA duct for the 0.25 and 0.9 inlet-velocity ratios. You will see that there are two separate graphs, one with a blue line and the other with an orange line. How to read these plots?

• Blue line (accumulated CD): represents the accumulated drag as we move along the x-axis. Therefore, the last value represents the total drag of the piece. Increasing values of drag imply a positive contribution coming from that area. On the other hand, a decreasing value represents a negative contribution coming from that area.
• Orange line (CD): represents the drag as we move along the z-axis. In this graph the value is not accumulated —I have done this because the drag vector is perpendicular to the z-axis—. Unlike the previous line trace; here a positive value represents a contribution to the drag while a negative value contributes thrust.

The drag is due to the combined contributions of the pressure distribution and the shear stress distribution over the body surface. In the images below we can see both the isolated contributions of pressure and shear stress $\tau$ as well as the net effects. As it could not be otherwise, the correlation between the graphs and the images is straightforward.

#### 0.25 inlet-velocity ratio

At low inlet-velocity ratios, the drag is negative, as Frick et al. predicted. There’s a high pressure area at the entry of the duct and in the lower half of the lip. Due to the ramp, this high pressure region is pushing the walls in the thrust direction while the lower lip in the drag direction. The core of the vortex is a low pressure region contributing to drag and the upper part of the lift provides some thrust as the flow accelerates back towards the free stream.

#### 0.90 inlet-velocity ratio

At higher velocity ratios the pictures is a slightly different one. Here the biggest contribution to drag is the lip due to the high pressure at the leading edge as a result of flow stagnation. Additionally, the upper left chart highlights a peak in drag at z = 0 m. That is due to shear stress —I’ve taken as part of the NACA duct the surface up to x = 0.422 m—; and although $\tau_x$ is smaller than $p$, it is acting over a larger surface. As in the previous case, there’s a high pressure region at the entry of the duct, but weaker due to a higher speed flow than before entering the duct.

## Conclusion

According to Frick et al. (1945), submerged inlets do not have desirable pressure recovery characteristics for use in supplying air to oil coolers, radiators, or carburettors of conventional reciprocating engines; but are most efficient in internal flow systems which require only a small amount of diffusion. CFD simulations already show a loss in total pressure of 14 to 25 % with respect to the free stream dynamic pressure.

The authors highlight a number of advantages, of which the most relevant to low-speed aerodynamics are the following:

1. Reduction of the length of internal ducting and elimination of bends.
2. Reduction in external drag when compared with external scoops.

But the disadvantages seem to weigh more and that’s why NACA-style submerged ducts have been disappearing. Just compare the image of the car that heads this article —a Ferrari F40 of 1987— with that of one of the most recent designs of the Italian brand —the Ferrari 488 Pista of 2018— shown in the video below.

We can see that Ferrari has put aside the use of NACA ducts, which have already been reduced in the Ferrari F50. Not only that, but the rear air intake that feeds the heat exchanger is not a completely submerged design, but protrudes from what would be the master surface of the door, seeking to combine the advantages of low drag of a submerged duct with that of a lower total pressure loss offered by a scoop. To this design, Ferrari also added boundary layer suction, a mechanism also studied by Frick et al. which improved the apparent pressure recovery at the end of the diffuser.

## References

Frick, C. W., Davis, W. F., Randall, L. M., & Mossman, E. A. (1945). An Experimental Investigation of NACA Submerged-Duct Entrances (Technical Report No. NACA-ACR-5I20). Moffett Field, CA, United States: National Advisory Committee for Aeronautics. Ames Aeronautical Lab.

Guerrero, J. (2016). A crash introduction to turbulence modeling in OpenFOAM. OpenFOAM® Introductory Course.

Mossman, E. A., & Randall, L. M. (1948). An experimental investigation of the design variables for NACA submerged duct entrances (Research Memorandum No. NACA-RM-A7I30). Moffett Field, CA, United States: National Advisory Committee for Aeronautics. Ames Aeronautical Lab.