Degradation of aerodynamic performances of two typical aerofoils under heavy rain: A comparative study using CFD simulation

During heavy rain, the lift force on airfoil structure is decreased, whereas, the drag is found to be increased. It has been reported that heavy rain up to 1500 mm/h may decrease the lift coefficient up to 20% and increase drag coefficient up to 30% (Haines et Luers, 1983). Heavy rain also affects premature boundary layer in low angle of attack and separation at high angle of attack. In aviation industries, optimized airfoil design capable of tolerating such adverse conditions of heavy rain emerges as a thrust domain of research in order to ensure flight safety and also to enhance its aerodynamic performances. Conventional simulation practice employs three-dimensional CFD models for effective performances of fluid-structure interaction (Emani et al., 2017). Similar trend of aerodynamic performances is also followed in comparative study for aerofoils. Basically rain happens in the low altitude at the time of take-off and landing. Aerodynamic efficiency is basically considered as the ratio of the lift coefficient to drag coefficient, which is degraded by 30-40% at the time of stalling in low altitudes. Here two different aerofoils have been considered for comparative analysis among different parameters under heavy rain situation.

Heavy rain is indicated by the LWC (Liquid Water Content) which is a function of rainfall intensity. For different rain conditions relationship between LWC and rain intensity varies (Joss et Waldvogal, 1969). The previous study of the aerodynamic performance degradation due to rain has been performed by Rhode (1941) who found 18% decrease in performance for the DC-3 aircrafts for LWC 50 g/m³. Haines and Luers (1983) analysed the frequency and intensity of very heavy rains and their effects on a landing aircraft. Hansman and Barsotti (1985) compared the aerodynamic performance degradation of NACA 64-210, NACA 0012, and Wortman FX 67-K170 aerofoils under the low Reynolds numbers in heavy rain conditions. In other similar wind tunnel experiments, laminar flow aerofoils were also found to experience performance degradation approximately equivalent to that caused by tripping the boundary layer to turbulence. On analysis of surface tension interaction of the water of intense rain, Bezos et al., (1992) noticed an aerodynamic degradation. Aerodynamic performance degradation depended on the location and diameter of the rivulet formation and rivulets. Valetine and Decker (1983) also studied the performance parameter of the NACA 64210 aerofoil by tracking the particles. Carlse and Hankey (1984) used two way coupled Euclerian scheme to model rain for NACA 0012 for fine and coarse rain. In fine rain condition, he found that the increase in drag and lift was a function of the fluid density, whereas for the coarse condition they did not find any effective changes.

Two approaches are used to model fluid particle Flow i.e. Euclidian and Langragian model. In Euclidian model, two fluids (basically uniform particle sizes) are taken and both particles and fluid are taken as continuous phase. For each flow, conservation equations are solved by considering the mass, phase exchange, momentum transfer energy transfer. In Langragian model, two approaches are used, one way coupled and two ways coupled. In one way coupled, the particle presence does not affect the trajectories of the continuous phase, but in the two way coupled motions both fluid and particles are interacting with each other. So source terms are added to solve the conservation equations. For the rain model, it is important to establish the size distribution of the water droplets. The wall temperature is responsible for the droplets to be splashed, rebound and stick.

In this present work, wall temperature is assumed to be below than the boiling temperature of the droplet, and only stick, spread and splash are considered here. As the experiment made by Bilanin (1987) described that the evaporation effect does not affect aerodynamic efficiency. So, we have ignored this effect. Therefore, only energy and momentum conservation equations are taken as the conservation equations for the film particles.

The assumptions are taken here are, the rain particles are non-reacting with each other and non-evaporative as per the past studies by Bilanin (1987). In accordance with the said study, evaporation of the droplets will not influence the aerodynamic performance. Non-deforming and spherical droplets are taken in present study for the simplification of the analysis, but in actual practice the raindrop deforms when they enter inside the boundary layer. For validation purpose XFOIL data was used. XFOIL is an interactive program for the design and analysis of subsonic isolated airfoils. XFOIL provides values of all performance parameters values as an output by taking Reynolds’s number and Mach number as input.

3.1. Scaling of the rain model

Rain is considered as heavy by taking two factors i.e. intensity and frequency of the rain. LWC is chosen for separating different intensity of the rain.

LWC can be written as:

$\left.L W C = \int _ { 0 } ^ { \infty } \rho _ { w } \frac { \pi } { 6 } D ^ { 2 } N ( D ) d D \right)$    (1)

Where, $\rho_w$ is the density of the water

Terminal velocity which is uniform under the action of gravity force and air friction drag force, is found to be a function of mean diameter of the particles and is given by Markowitz (1976) as follows:

$\mathrm { V } ( \mathrm { D } ) = 9.58 \left[ 1 - \operatorname { Exp } \left\{ - \left( \frac { D } { 1.77 } \right) ^ { 1.147 } \right\} \right]$    (2)

Where, D is the mean diameter of the particle. A correction for the aloft is given by Markowitz (1976) as follows:

$\mathrm { V } ( \mathrm { D } ) = \mathrm { V } _ { 0 } ( \mathrm { D } ) \left( \frac { \rho _ { 0 } } { \rho _ { a } } \right) ^ { 0.4 }$    (3)

Where, V₀ (D) is the terminal velocity of the particle when density of the air loft is $\rho_0$.

3.1.1. Wall film model

In this model, some assumption has been taken for the easy simulation in software.  Basically this model is used to describe the various interactions between rain drops and boundary surface. This interaction includes drop impingement, momentum transfer, droplet evaporation and splashing effect, mass transfer, conduction and convective heat transfer, flow separation etc. The assumption, that have been taken here, are as follows:

1) The water film layer is very thin.

2) The temperature of the film is below the boiling temperature of the water particle.

3) Film particles are assumed to be direct contact with the wall surface so that only conduction heat transfer is possible

The wall temperature is responsible for the droplets to be splashed, rebound, spread and stick. In this case, as the wall temperature is assumed to be below than the boiling temperature of the droplet so only stick, spread and splash are considered here. As the experiment made by Bilanin (1987) described that the evaporation effect does not affect aerodynamic efficiency. Therefore, this effect was ignored this effect. So, only energy and momentum conservation equations were considered in the conservation equations for the film particles. ICEM CFD was used for geometry and hexagonal mesh generation. k-$\in$RNG models was chosen. Forair, ideal gas model has been used which includes both compressibility and Sutherland law as viscosity model. The second order upwind scheme and second order momentum schemes have been used for discrimination to reach at the final result. The governing equations are used here are as follows:

$\frac { \partial \rho } { \partial t } + \frac { \partial \left( \rho u _ { i } \right) } { \partial x _ { i } } = 0$     (4)

$\frac { \partial \rho u _ { i } } { \partial t } + \frac { \partial \left( \rho u _ { i } u _ { j } \right) } { \partial x _ { j } } = - \frac { \partial p } { \partial x _ { i } } + \frac { \partial \left[ \mu \left( \frac { \partial u _ { i } + \partial u _ { j } } { \partial x _ { i } }- \frac { 2 } { 3 }\rho_i \frac { \partial u _ { i } } { \partial x _ { i } } \right) \right] } { \partial x _ { j } } + \frac { \partial ( - \rho \overline { u _ { i } ^ { \prime } u _ { j } ^ { \prime } } ) } { \partial x _ { j } }$   (5)

$- \rho \overline { u _ { \imath } ^ { \prime } u _ { \jmath } ^ { \prime } }$ is Reynolds stress term and k-$\in$turbulent model equations are as follows:

$\frac { \partial ( \rho k ) } { \partial t } + \frac { \partial \left( \rho k u _ { j } \right) } { \partial x _ { j } } = \frac { \partial \left( \alpha _ { k } \mu _ { e f f } \frac { \partial k } { \partial x _ { j } } \right) } { \partial x _ { j } } + G _ { k } + G _ { b } - \rho \in - Y _ { m } + S _ { k }$   (6)

$\frac { \partial ( \rho \in ) } { \partial t } + \frac { \partial \left( \rho \in u _ { j } \right) } { \partial x _ { j } } = \frac { \partial \left( \alpha _ { k } \mu _ { e f f } \frac { \partial k } { \partial x _ { j } } \right) } { \partial x _ { j } } + C _ { 1 \in } \frac { \epsilon } { k } \left( G _ { k } + C _ { 3 \in } G _ { b } \right) - C _ { 2 \in } \rho \frac { \epsilon ^ { 2 } } { k } - R _ { \in } + S _ { k }$     (7)

3.1.2. Two phase modelling

Currently two approaches are being used as Eulerian-Eulerian and Eulerian-Langrangian. In present case, Eulerian-Langrangian approach has been used. This approach treats the fluid as the continuous phase and the particles as the dispersed phase. The particles are tracked, which can exchange as, momentum, energy with the continuous phase. Dispersed phase occupies low volume fraction and high mass flow rate. The track of the dispersed particles can be computed by using the acceleration produced by the force balance equation on the particles, which can be written as follows:

$\frac { d v _ { p } } { d t } = F _ { \text {Drag } } \left( v - v _ { p } \right) + F _ { x }$ (8)

F_x is the additional acceleration term.

F_Drag is drag force per unit mass and written as

$F _ { \text {Drag} } = \frac { 18 \mu C _ { d } R e } { 24 \rho p d _ { p } ^ { 2 } }$     (9)

Where, v is the fluid velocity, v_p is the particle velocity, $\mu$ is the molecular viscosity of the fluid,

$\operatorname { Re } = \frac { \rho d _ { p } \left| v _ { p } - v \right| } { \mu }$       (10)