3. Case studies

Air cooling is accomplished by air flowing into the engine compartment through openings in front of the engine cowling. Expulsion of the hot air occurs through one or more openings in the lower portion of the engine case. The air cooling system is less effective during ground operations, takeoffs, go-arounds, and other periods of high-power, low-airspeed operation. The engine should not operate at higher than its designed temperature because of loss of power and excessive oil consumption, see a list of engine typologies in Figure 5. Two case studies are presented in the following subsections regarding the best possible mass flow rate ensuring the reduction of the temperature under critical flight conditions.

Figure 5. Different typologies of aviation engines.

#### 3.1. Heat exchanger efficiency in a pusher engine

We verify here the air flow rate efficiency of an aircraft oil cooling system. The objective of this analysis is the computation of the mass flow rate useful for a regional new concept pusher engine aircraft under cruise conditions. A simplified geometry is used in order to adopt a porous medium numerical model. This tool allows to model the pressure losses and the heat transfers using the input parameters of a software package for a Darcy-Forchheimer porous material. The mass flow rate to be achieved in order to reduce the engine temperatures is

m, mass flow rate target = 0.25 kg/s

The following table illustrates the heat exchanger performances:

The flow condition (cruise) has the following characteristics:

• Mach, M<sup>∞</sup> = 0.28

3. Case studies

160 Heat Exchangers– Advanced Features and Applications

Figure 5. Different typologies of aviation engines.

Air cooling is accomplished by air flowing into the engine compartment through openings in front of the engine cowling. Expulsion of the hot air occurs through one or more openings in the lower portion of the engine case. The air cooling system is less effective during ground operations, takeoffs, go-arounds, and other periods of high-power, low-airspeed operation. The engine should not operate at higher than its designed temperature because of loss of power and excessive oil consumption, see a list of engine typologies in Figure 5. Two case studies are presented in the following subsections regarding the best possible mass flow rate

ensuring the reduction of the temperature under critical flight conditions.


The classical Darcy-Forchheimer law for porous materials reads:

$$\frac{\Delta p}{L} = \frac{\mu}{K}v + \frac{\rho}{2}C\_2v^2 = av + bv^2\tag{18}$$

where K is the permeability of the material, μ is the related dynamic viscosity, a is the Darcy coefficient, and b is the inertial Forchheimer coefficient. The relationship between the mass flow rate m\_ and pressure drop Δp in the cooler can be put in a similar shape, see the values shown in Table 2. Nevertheless, as indicated in equation Eq. (18), viscous and inertial resistances are completed as follows:

Viscous resistance

$$20.598 = \frac{\mu}{K} \Delta n \quad \rightarrow \ a = 5426501.18 \text{ 1/m}^2 \tag{19}$$

Inertial resistance

$$2.1355 = C\_2 \frac{1}{2} \rho \Delta n \to b = 23.10 \text{ 1/m} \tag{20}$$

where Δn is the HE total length in the flow direction, ρ is the air density, and μ is the air dynamic viscosity, see papers [23–26]. By using the aforementioned values, one can simulate the external and internal flow fields with respect to the cooling ducts and find the numerical air flow rate passing through the heat exchanger. In this manner, one can establish if the aforementioned target is achieved or not and, in this last case, choose another heat exchanger.


Table 2. Characteristic values of the heat exchanger taken into consideration.

#### 3.2. Compact heat exchangers choice for a light helicopter

Often the choice of the heat exchanger positioning can be crucial in a life of a helicopter. In the following, a number of simulations are presented tailored to the best cooler location for a light helicopter. The flow equations are solved by means of a finite volume code and a structured grid generator.

Three positions for the heat exchanger location have been investigated by a thermal point of view as shown in Figure 6. Each position is characterized by a specific value of air flow rate. In order to maximize the flow rate and taking into account also maintenance problems, the manufacturer chooses to locate the cooler near the opening after the engine because the cooler is crossed by a mass flow rate able to cool the engine and can be inspected by the maintenance team. Using the same methodology of the previous paragraph, the designer, in a simplified manner, and without knowing the constructive details of the heat exchanger, can so take preliminary decisions about the size and the positioning of the heat exchanger reducing the number of certification tests and the related cost, see also paper [25].

Figure 6. Light helicopter side view with heat exchanger locations.
