Numerical Simulation of Hot Air Anti-Icing Characteristics for Intake Components of Aeronautical Engine

Abstract

A three-dimensional numerical simulation of hot air anti-icing was conducted on the full-annular realistic model of engine intake components, comprising the intake ducts, intake casing, struts, axial flow casing, and zero-stage guide vanes, based on the intermittent maximum icing conditions and the actual engine operating parameters. The simulation integrated multi-physics modules, including air-supercooled water droplet two-phase flow around components, water film flow and heat transfer on anti-icing surfaces, solid heat conduction within structural components, hot air flow dynamics in anti-icing cavities, and their coupled heat transfer interactions. Simulation results indicate that water droplet impingement primarily localizes at the leading edge roots and pressure surfaces of struts, as well as the leading edges and pressure surfaces of guide vanes. The peak water droplet collection coefficient reaches 4.2 at the guide vane leading edge. Except for the outlet end wall of the axial flow casing, all anti-icing surfaces of intake components maintain temperatures above the freezing point, demonstrating effective anti-icing performance. The anti-icing characteristics of the intake components are governed by two critical factors: cumulative heat loss along the hot air flow path and heat load consumption for heating and evaporating impinging water droplets. The former induces a 53.9 °C temperature disparity between the first and last struts in the heating sequence. For zero-stage guide vanes, the latter factor exerts a more pronounced influence. Notable temperature reductions occur on the trailing edges of three struts downstream of the hot air flow and at the roots of zero-stage guide vanes.

1. Introduction

The intake components of an aeronautical engine (the mainstream modern aeronautical engine centered on gas turbine technology) refer to the intake system upstream of the compressor, principally comprising the intake ducts, casing, struts, and guide vanes (zero-stage guide vanes). These components exhibit intricate aerodynamic interactions and cooperative functions to ensure the continuous and steady ingress of air flow into the compressor. During aircraft operation in clouds with supercooled water droplets (water droplets remain in a liquid state despite having a temperature below 0 °C), these droplets impinge upon the windward surfaces of engine intake components and freeze into ice [1]. The ice accretion on component surfaces deteriorates the aerodynamic performance of the engine and reduces thrust, significantly affecting the normal flight of the aircraft. Moreover, the shedding of ice layers from components such as guide vanes can damage the compressor blades, causing mechanical damage to the compressor and posing a severe threat to flight safety [2]. To ensure safe and efficient aircraft operation, anti-icing systems are installed on components susceptible to icing. Owing to their simple structure, low maintenance cost, and high efficiency, air thermal anti-icing systems using hot air as the heat source are currently predominant in aircraft applications. Hot air extracted from the engine compressor transfers heat to the outer surfaces of anti-icing components via solid heat conduction, maintaining temperatures above the freezing point to prevent ice formation. For the anti-icing cavities of aeronautical engine intake components, structural designs are typically based on the overall icing characteristics, with the cavities of individual components interconnected and mutually constrained. Therefore, investigating the integrated hot air anti-icing characteristics of the intake components holds significant importance for ensuring the normal operation of the engine and the flight safety of the aircraft.

Hot air anti-icing is a complex process involving multi-physics field coupling, encompassing several physical modules such as the flow and heat transfer of air-supercooled water droplet two-phase flow outside components, the water film flow and icing phase change on component surfaces, the solid heat conduction inside components, and the flow and heat transfer of hot air in hot air anti-icing cavities. Currently, research on air-supercooled water droplet two-phase flow as well as water film flow and icing phase change on component surfaces is relatively mature. In numerical studies of two-phase flow fields, based on the dilute flow characteristics of supercooled water droplets in air, scholars have mainly focused on modeling methods such as the Euler–Lagrange method [3,4,5] and the Euler–Euler method [6,7,8]. Among them, some studies based on the Euler–Lagrange method involve two-way coupling between the two phases, but this method requires excessive computational effort in three-dimensional applications and involves cumbersome coordinate transformations. The Euler–Euler method, on the other hand, has been widely used in current three-dimensional numerical studies. For research on water film flow and icing phase change on component surfaces, most scholars’ mathematical descriptions of water film flow and heat transfer are based on the Shallow Water Icing Model (SWIM), which assumes that the water film flow is laminar [9,10]. However, since hot air anti-icing involves the aforementioned multi-physics fields and their coupling, numerical simulations of hot air anti-icing have undergone a transition from simplifying some processes to considering the full physical processes.

Early numerical simulations of hot air anti-icing by both domestic and international scholars often neglected the full physical processes involved and relied on simplified assumptions. For instance, Dong Wei et al. [11] studied the wall temperature distribution of zero-stage guide vanes under anti-icing conditions by specifying wall heat flux, which omits calculations for solid heat conduction. Chen Weijian et al. [8] investigated the hot air anti-icing characteristics of guide vanes, and Tang Guancai et al. [12] studied intake struts; however, both studies excluded the physical processes of water film flow and icing phase change. Qin Na et al. [13] examined the heat transfer characteristics of hot air anti-icing cavities in nacelle inlets, neglecting processes such as water droplet impingement, water film flow, and icing phase change. With advances in understanding anti-icing mechanism, recent numerical studies have begun to simulate hot air anti-icing under oncoming flow conditions containing supercooled water droplets, accounting for processes such as water droplet impingement, water film flow, and icing phase transitions. Studies by Wang Kun et al. [6], Yang Yi et al. [7], and Bu Xueqin et al. [14] all focused on aircraft wings and analyzed the anti-icing characteristics under the full physical processes of hot air anti-icing. Mahmoudi et al. [15] focused on the gas turbine intake system and carried out numerical simulations, incorporating the complete physical processes of anti-icing, to study the influence of various anti-icing structures on the hot air anti-icing characteristics. It is evident that the numerical simulations of hot air anti-icing considering full physical processes have become the mainstream research direction both domestically and internationally.

In terms of components involved in anti-icing research, numerical studies on hot air anti-icing characteristics by domestic and international scholars have predominantly focused on aircraft wings [16,17,18,19,20,21,22,23,24]. For example, Abdelghany et al. [16] investigated the influence of hot air extraction parameters on wing anti-icing performance, while Ni Zhangsong et al. [19] studied the effect of environmental parameters. Research by Rigby [17], Saeed [18], and Pellissier et al. [24] concentrated on the impact of anti-icing cavity structures on wing anti-icing behavior, whereas Gu Hongyu et al. [21] studied the formation of runback ice on wing surfaces under hot air anti-icing conditions. In the field of anti-icing research for aeronautical engine intake components, research has primarily concentrated on individual components such as intake ducts and their lips [25,26,27,28,29,30], intake struts [31,32,33,34,35], and guide vanes (zero-stage guide vanes) [36,37,38]. For instance, Zhang Shuye et al. [28] and Niu Xinlong et al. [29] conducted numerical studies on hot air anti-icing for inlet lips, exploring the influence of anti-icing cavity structural parameters and hot air extraction parameters on anti-icing performance. Regarding the hot air anti-icing characteristics of intake struts, Li Yundan [33] indicated in his research that the anti-icing surface temperature at the strut trailing edge under anti-icing conditions is relatively low, suggesting it to be an icing-prone area. For the zero-stage guide vanes, Wang Bo et al. [36] carried out relevant studies and reported that the highest anti-icing surface temperature occurs at the central part of the vane near the hot air inlet, while the lowest temperature is located at the root.

Building upon the preceding analyses, significant research gaps remain regarding the hot air anti-icing characteristics of aeronautical engine intake components that fully account for the relevant physical processes, a critical aspect for the design of high-efficiency anti-icing systems of aeronautical engines. Therefore, this study presents a numerical investigation into the hot air anti-icing performance of engine intake components (encompassing intake ducts, intake casings, struts, zero-stage guide vanes, and axial flow casings) under intermittent maximum icing conditions. Utilizing commercial numerical platforms, this study incorporates realistic engine operational parameters and adopts a multi-physics coupling framework that integrates external air–supercooled water droplet two-phase flow, water film flow and icing phase change on anti-icing surfaces, solid heat conduction within structural components, and the heat transfer of hot air streams. Through this integrated approach, this study quantifies the spatial distribution of droplet impingement dynamics and anti-icing surface thermodynamics across intake components, thereby providing critical insights for the experimental validation of anti-icing performance and the optimal design of advanced anti-icing systems.

2. Anti-Icing Numerical Calculation Method and Validation

2.1. Computational Module Composition

The numerical simulation of hot air anti-icing involves four core computational modules: air flow field, water droplet flow field and impingement, water film flow and icing phase change, and solid heat conduction.

2.1.1. Air Flow Field Calculation

ANSYS CFX is employed to simulate the aerodynamic fields in both external and internal regions of components by solving the three-dimensional, steady-state Navier-Stokes (N-S) equations for viscous flows. The air flow field is simulated using the Shear Stress Transport (SST) k-ω turbulence model for turbulence modeling. This numerical approach enables the calculation of air flow fields within the main flow passages of the intake components, hot air pipelines, and anti-icing cavities, along with the temperature distributions within solid structures.

2.1.2. Water Droplet Flow Field and Impingement Calculation

Given the small particle size of supercooled water droplets and their low content in air, the influence of supercooled water droplets on air flow is neglected in the calculation, with only the one-way effect of air on droplets considered between air and supercooled water droplets [39,40]. An Eulerian approach is adopted for simulating the water droplet flow field and impingement characteristics. The governing equations for the water droplet phase are solved based on the precomputed air flow field results to obtain the spatial distributions of droplet velocity and liquid water content (LWC, defined as the mass of water droplets per unit volume of air flow).

The local droplet collection coefficient $\beta$ is defined as follows:

$$\beta ={\displaystyle \frac{{\rho }_d{\alpha }_d}{LWC}}{\displaystyle \frac{V_{d}n}{\left|V_{d,\infty }\right|}}$$

(1)

where ${\rho }_d$ and ${\alpha }_d$ represent the droplet density and the droplet volume fraction at the impingement location, respectively, whose product yields the local liquid water content at the impingement; $LWC$ is the incoming liquid water content; $V_d$ and $V_{d,\infty }$ are the droplet velocity vector at the impingement surface and of incoming flow; and $n$ is the outward-pointing unit normal vector of the impingement surface.

2.1.3. Water Film Flow and Icing Phase Change Calculation

When supercooled water droplets impact the surface of anti-icing components, they typically form a thin water film that flows along the surface driven by aerodynamic shear forces. Depending on thermodynamic conditions, the water film may freeze or evaporate on the component surface. Figure 1 illustrates the heat and mass transfer phenomena occurring within the control volume of an anti-icing micro-element, where $x=\left(x_1,x_2\right)$ denotes the coordinate along the surface and the y represents the coordinate normal to the surface. In the figure, the purple lines represent the anti-icing surface, the blue lines represent the water film on the component surface, and the orange lines represent the velocity gradient within the water film. During the anti-icing process, due to the thinness of the water film and its low flow velocity, the water film flow on the surface of the intake components is considered to be laminar flow [9,10]. Accordingly, the conservation equations for water film momentum, mass, and energy are established.

(1)

Conservation equation for momentum

Assuming that the water film is driven exclusively by aerodynamic shear forces and its velocity exhibits a linear distribution across the film thickness (as depicted in Figure 1), the momentum equation for the water film can be simplified as follows:

$$V_f\left(x,y\right)={\displaystyle \frac{y}{{\mu }_f}}{\tau }_{a,wall}\left(x\right)$$

(2)

where $V_f$ is the velocity of water film; ${\mu }_f$ is the dynamic viscosity of water; and ${\tau }_{a,wall}$ is the aerodynamic shear stress exerted on the water film.

(2)

Conservation equation for mass

During the flow of water film over anti-icing surfaces, mass is introduced through supercooled water droplet impingement and inflow from adjacent control volumes, while mass loss occurs due to evaporation, freezing, and outflow to adjacent volumes. The mass conservation equation for the water film is, thus, expressed as follows:

$${\rho }_f\left[{\displaystyle \frac{\partial h_f}{\partial t}}+\nabla \left(V_f{h}_f\right)\right]=V_{d,\infty }\left(LWC\right)\beta -{\dot{m}}_{evap}-{\dot{m}}_{ice}$$

(3)

where ${\rho }_f$ and $h_f$ are the density and the height of water film, respectively; t represents time; and ${\dot{m}}_{evap}$ and ${\dot{m}}_{ice}$ are the mass flow rate of water evaporation and freezing per unit area, respectively.

(3)

Conservation equation for energy

During the anti-icing process, energy transfer and transformation in the water film are primarily driven by heat conduction, evaporation, and icing phase change. The energy conservation equation for the water film is, thus, formulated as follows:

$$\begin{gathered} {\rho }_f\left[{\displaystyle \frac{\partial h_f{c}_f{T}_f}{\partial t}}+\nabla \left(V_f{h}_f{c}_f{T}_f\right)\right]=\left[c_f\left(T_{\infty }-T_f\right)+{\displaystyle \frac{1}{2}}{V}_d^2\right]V_{d,\infty }\left(LWC\right)\beta \\ -{\dot{m}}_{evap}{L}_{evap}-{\dot{m}}_{ice}\left(L_{fus}-c_{ice}{T}_f\right)+Q_{conv}+Q_{anti} \end{gathered}$$

(4)

where $c_f$ and $c_{ice}$ are the specific heat capacity of water and ice; $T_{\infty }$ and $T_f$ are the temperature of incoming flow and anti-icing surfaces; $L_{evap}$ and $L_{fus}$, respectively, are latent heat of vaporization and freezing for water; $Q_{conv}$ represents the convective heat transfer between the external air flow and the water film; and $Q_{anti}$ denotes the heat supplied by the anti-icing system.

The velocity of water film $V_f$ is first derived from the momentum Equation (2), which is then substituted into the mass conservation Equation (3) and energy conservation Equation (4). By integrating the compatibility relationship [41] among the height of water film $h_f$, the temperature of anti-icing surfaces $T_f$, and the mass flow rate of water freezing per unit area ${\dot{m}}_{ice}$, the three unknowns are solved.

2.1.4. Solid Heat Conduction Calculation

Heat is transferred from the inner surface to the outer surface of anti-icing components through solid heat conduction, governed by the following conduction equation:

$${\rho }_s{c}_s{\displaystyle \frac{\partial \left(\Delta T\right)}{\partial t}}=\nabla \cdot \left[\lambda \left(T\right)\nabla \left(\Delta T\right)\right]-{\rho }_s{\displaystyle \frac{\Delta H}{\Delta T}}$$

(5)

where ${\rho }_s$ and $c_s$ are the density and the specific heat capacity of the solid; $\Delta T$ is the temperature variation at a given node during the iteration process; $\lambda$ is the thermal conductivity coefficient of the solid; and $\Delta H$ is the enthalpy change in the solid.

The discretization methods for different variables and the solution methods for partial differential equations in each calculation module are detailed in Reference [42].

2.2. Computational Process

This study presents a numerical simulation of hot air anti-icing for engine intake components using CFX and FENSAP-ICE software of ANSYS 2023. The computational process consists of two stages: one is flow field and initial ice accretion calculation without solid heat conduction, whose results serve as the initial conditions for coupled iteration; the other is coupled iterative calculation considering solid heat conduction, while assuming the unchanged water droplet flow field and impingement characteristics. The second stage achieves the thermal equilibrium calculation among physical modules by continuously updating heat fluxes and temperatures at the interfaces of air, water film, and solid walls. The detailed computational workflow is documented in Ref. [42].

2.3. Computational Method Validation

Due to the lack of available experimental data for the hot air anti-icing of engine intake components, this study selects an engine intake strut for simulation and compares the numerical results with the experimental data from Ref. [31] to validate the calculation method. The aerodynamic configuration of the strut and the structure of its hot air anti-icing cavity are similar to those of the struts in the intake components studied in this work. The physical model is illustrated in Figure 2, where the spanwise cross-section gradually shrinks from the strut root to the tip. A hot air anti-icing cavity is positioned along the leading edge, extending through the entire span of the strut. Figure 3 depicts the mid-span cross-section A-A perpendicular to the strut span, from which the anti-icing surface temperatures for experimental comparison are extracted.

Table 1. Validation cases of hot air anti-icing.

Case	${\mathit{V}}_{\mathit{a}\mathit{i}\mathit{r}}$ (m/s)	${\mathit{T}}_{\mathit{a}\mathit{i}\mathit{r}}$ (°C)	LWC (g/m3)	MVD (μm)	${\dot{\mathit{m}}}_{\mathit{h}\mathit{o}\mathit{t}}$ (g/s)	${\mathit{T}}_{\mathit{h}\mathit{o}\mathit{t}}$ (°C)
1	59.4	−11.9	1.0	20	5.9	149.9
2	58.2	−5.9	2.0	20	5.9	150.7

presents the operating parameters for the validation cases of hot air anti-icing, where the inflow velocities $V_{air}$ in the two cases are close to 59.4 m/s and 58.2 m/s, respectively. The median volumetric diameter (MVD) of supercooled water droplets and the hot air flow rate ${\dot{m}}_{hot}$ remain identical for both cases, at 20 μm and 5.9 g/s, while other parameters such as inflow temperature $T_{air}$, inflow liquid water content (LWC), and hot air inlet temperature $T_{hot}$ differ between the cases.

Figure 4 depicts the comparison of anti-icing surface temperatures on the mid-section A-A of the strut for Case 1 and Case 2, where the red curve represents the calculated results and the blue dots denote the experimental data. As indicated in the figure, the calculated anti-icing surface temperature distributions from the strut’s leading edge to trailing edge are consistent with the experimental data. For Case 2, the calculated temperatures at all seven measuring points closely match the experimental results, while Case 1 exhibits significant errors only at the first two measurement points. This indicates that, under conditions of higher ambient temperature and larger liquid water content (LWC), the hot air anti-icing calculation results demonstrate better agreement with experimental data. Further data analysis reveals that the average errors of the calculated anti-icing surface temperatures at the seven measurement points for the two cases are 0.76 °C and 0.95 °C, respectively. Therefore, the anti-icing calculation method adopted in this paper demonstrates high accuracy.

3. Physical Model

Figure 5 presents the physical model structure of the aeronautical engine intake component studied in this paper (from the perspective of the model’s outflow port). The intake components primarily consist of intake ducts, intake casing, struts, zero-stage guide vanes, and an axial flow casing. All components except the struts are thin-walled structures. Five circumferentially and non-periodically spaced struts are positioned inside the intake casing, while 18 periodically spaced zero-stage guide vanes are connected to the axial flow casing. The attack angle of the guide vanes relative to the incoming flow varies with different engine operating conditions.

For an aeroengine, the hot air anti-icing system functions as a complex integrated whole: none of the components or their anti-icing cavities operate independently. Instead, the anti-icing cavities of all components are interconnected and work in collaboration to achieve the desired anti-icing performance. Figure 6 illustrates the hot air anti-icing system for the engine intake components. The hot air inlet is positioned on the intake casing. Upon entering the anti-icing cavity, the hot air splits into two branches: the front branch heats the intake casing and struts, discharging through two circumferential rings of air vents (sequentially numbered as Outlet 1–3 in the order from the tip to the root) at the front end of the intake casing, where it mixes with the main cold air flow; the rear branch flows upward along the axial flow casing, heating the casing and zero-stage guide vanes, and exits through three air vents in each guide vane to merge with the main air flow. The hot air anti-icing cavity within each strut is located along the leading edge, extending across the entire span of the strut. The anti-icing cavity within the zero-stage guide vanes features a ring-shaped structure, with hot air entering through two air inlets at the vane tips.

Anti-icing surfaces (i.e., the outer surfaces of heated walls of components) are categorized according to component types and their positions, including the windward/leeward sides of the intake casing, outer/inner supports of struts, struts, zero-stage guide vanes, and axial flow casing. Struts and guide vanes are numbered according to the heating sequence of hot air flow. The specific anti-icing surfaces and numbering scheme are presented in Figure 7, where, from the upstream view of the zero-stage guide vanes, the left-half guide vanes are numbered clockwise as L1–L9 and the right-half guide vanes are numbered counterclockwise as R1–R9.

4. Computational Model and Grid Generation

4.1. Computational Domain and Boundary Conditions

Figure 8 illustrates the fluid computational domain of the intake components consisting of two parts: the cold air flow main passage domain and the hot air flow path domain. The cold air flow main passage domain is bounded by the intake duct inlets, outer walls of intake components, side vents of intake ducts, axial flow casing outlet (i.e., engine inlet), and hot air outlet on the axial flow casing and zero-stage guide vanes. The hot air flow path domain is enclosed by the inlet of hot air anti-icing cavity, anti-icing cavity walls, outlets on intake casing, and zero-stage guide vane. The two domains are connected via interface surfaces. To improve computational convergence, the axial flow casing flow path is extended in the oncoming direction, with an extension length approximately five times the span of the zero-stage guide vanes. The solid computational domain comprises the intake casing (including struts), axial flow casing, and zero-stage guide vane.

The boundary conditions for the air flow computational domain are defined as follows: the intake duct inlets are set as mass flow inlets with the oncoming flow temperature specified; the side vents of intake ducts are set as mass flow outlets; the axial flow casing outlet serves as a pressure outlet with the static pressure specified; and the hot air inlet is designated as a total pressure inlet with the temperature specified. For the supercooled water droplet flow field, the incoming liquid water content (LWC) and median volumetric diameter (MVD) are specified based on the air flow field boundary conditions.

During the anti-icing coupled iterative calculation, the computational domain comprises fluid and solid domains, where the anti-icing surfaces within the solid domain act as fluid–solid coupling interfaces with their temperatures updated iteratively, and all other walls in the solid domain are treated as adiabatic boundaries.

4.2. Grid Generation and Independence Verification

The cold air flow main passage domain, hot air flow path domain, and solid domain are discretized using unstructured tetrahedral grids generated by ANSYS ICEM. To accurately capture the complex flow and heat transfer characteristics within the wall boundary layer, local mesh refinement is applied in the near-wall region. To ensure grid scale compatibility with the Shear Stress Transport (SST) k-ω turbulence model, the first-layer mesh height is set to 0.01 mm, corresponding to y⁺ ≈ 1.

To evaluate the influence of grid density on calculation results, five sets of grids with total grid numbers of 32 million, 38 million, 43 million, 49 million, and 54 million are used to verify grid independence for the hot air anti-icing calculation model of the intake components. Taking the windward side of the intake casing as an example, Figure 9 presents the temperature distributions of the anti-icing surface under different total grid quantities. It can be observed from the figure that, when the total grid quantities are 43 million, 49 million, and 54 million, the temperature distributions of the anti-icing surface remain basically consistent. Specific points on the windward and leeward sides of the intake casing, the strut, and the zero-stage guide vanes are selected as monitoring points to monitor their anti-icing surface temperatures. The variation of the anti-icing surface temperature at each point with the total grid quantity is demonstrated in Figure 10. Using the monitoring point data of 54 million grids as the reference, Figure 11 depicts the absolute errors of the anti-icing surface temperature at the monitoring points under each set of grids. The results indicate that, when the total grid number exceeds 43 million, the anti-icing surface temperatures at all positions remain essentially unchanged with a further increase in grid number. Therefore, a computational grid consisting of approximately 43 million cells is adopted in this study.

The solid domain grids (gray), hot air flow path grids (red), and cold air flow main passage domain grids (blue) for the front end of intake casing, struts, axial flow casing, and zero-stage guide vanes are illustrated in Figure 12. Among them, B-B in the right subfigure of Figure 12b indicates the cross-section of the left subfigure.

4.3. Computational Case

In accordance with the icing meteorological conditions specified in Appendix C of the Airworthiness Standards for Transport Category Airplanes (CCAR-25) [43] issued by the Civil Aviation Administration of China (CAAC), and combined with the icing critical points of an engine intake system analyzed by Song Jianyu et al. [44], this paper selects a typical intermittent maximum icing condition at an altitude of 1200 m, characterized by “ambient temperature of −5 °C, liquid water content (LWC) of 2.4 g/m³, and median volumetric diameter (MVD) of 20 μm”. Meanwhile, the engine operating condition is matched to the maximum continuous state based on the engine operating envelope, the flight Mach number is determined as 0.3 by the most economical flight speed, and the hot air bleeding parameters are determined accordingly. The parameters of the computational case are listed in

Table 2. Parameters of the computational case.

Parameter		Value
icing meteorological parameters	ambient temperature/°C	−5
	LWC/(g/m3)	2.4
	MVD/μm	30
engine and flight operating parameters	altitude/m	1200
	flight Mach number	0.3
	engine operating condition	maximum continuous
hot air bleeding parameters	mass flow rate/(g/s)	71
	temperature/°C	320

. Under this condition, the angle of attack between the zero-stage guide vane and the axial air flow passage is 3.5°.

5. Results and Analysis

This paper analyzes the calculation results in three aspects: air flow field, supercooled water droplet flow field and water droplet impingement characteristics, and anti-icing characteristics. The mid-section of flow field and the strut employed in the analysis are depicted in Figure 13. The mid-section of flow field is a plane passing through the symmetry line of the intake duct inlet and parallel to the axis of the axial flow casing. The mid-section of the strut is a cross-section perpendicular to its spanwise direction, located at the mid-span.

5.1. Air Flow Field

As presented in Figure 14, the velocity distribution of air on the mid-section reveals that the cold air flow within the main flow passage progressively accelerates as it flows from the intake duct inlets. This acceleration is primarily driven by the converging flow path, becoming most significant within the axial casing channel. In the bypass channels of intake ducts, the deflection of the flow at the bypass inlet induces a low-velocity recirculation zone near the entrance. Further downstream, the narrowing bypass causes the flow to re-accelerate before it exits through the side vents.

Due to the significantly smaller geometry of the hot air flow path compared to the main flow passage, local magnification and streamline densification are performed to analyze the air flow velocity distribution, especially at the hot air outlets of the intake casing and within the hot air cavities of zero-stage guide vanes on the mid-section. At the hot air outlets of the intake casing, the abrupt contraction of the flow channel causes a significant acceleration of the hot air, reaching up to 450 m/s. The discharged hot air adheres to the wall surface due to the influence of the main cold air flow, while the hot air causes the cold air in the main flow passage to converge toward the channel center. When hot air in the axial flow casing pipeline enters the annular hot air cavity of zero-stage guide vanes, the flow accelerates due to the abrupt contraction at the inlet and splits into two branches directed toward the vane leading edge and trailing edge, respectively. Most of the hot air flowing toward the trailing edge exits through Outlet 1, with the remaining air continuing to flow toward the vane root; the hot air branch toward the leading edge is ejected at high velocity driven by the lower pressure at Outlet 3, which results in reduced flow velocity near the bottom of the annular cavity.

The streamwise pressure distribution in the main flow passage is illustrated in Figure 15. From the intake duct inlets to the side vents, the air pressure initially rises before decreasing. The initial pressure rise corresponds to a low-velocity zone within the bypass channel, while the subsequent pressure drop is caused by the channel’s downstream contraction. Correspondingly, the air pressure in the intake casing exhibits a gradual decrease along the flow direction, consistent with the increasing flow velocity. The initial pressure rise corresponds to a low-velocity zone within the bypass channel, while the subsequent pressure drop is caused by the channel’s downstream contraction. Specifically, the pressure side of each strut exhibits higher pressure than the suction side, with this disparity being most pronounced at the strut leading edges. For the flow passage near zero-stage guide vanes, the channel area contraction induced by the vanes increases flow velocity, resulting in corresponding pressure reduction.

5.2. Supercooled Water Droplet Flow Field and Impingement Characteristics

Figure 16 illustrates the velocity distributions of supercooled water droplets on the mid-section of the intake ducts and intake casing flow channels, as well as Section 1 and Section 2, which are cross-sections perpendicular to the flow direction, adjacent to the leading edges of the struts and zero-stage guide vanes, respectively. The contour values on the mid-section represent the magnitude of droplet velocity, while those on Section 1 and Section 2 denote the velocity component normal to the plane and the streamlines indicate the velocity directions of droplets on the planes. Figure 17 presents the streamwise distribution of liquid water content (LWC) for supercooled water droplets in the main flow passage.

As depicted in Figure 16a, the supercooled water droplets are entrained by the air flow and, consequently, their velocity distribution is generally consistent with that of the air itself. Specifically, droplet velocity gradually increases from the intake duct inlets to the axial flow casing outlet; it also re-accelerates after traversing through the low-velocity zone in the bypass channels.

An analysis of the droplet velocity and liquid water content (LWC) distributions indicates that upstream intake duct bifurcation exhibits a uniform distribution of both properties. Near the bifurcation, the flow diversion by bypass causes water droplets to converge toward the windward side of the intake casing, resulting in higher LWC at the windward side near the intake casing inlets, as illustrated in the frontmost part of the intake casing in Figure 17b.

After supercooled water droplets enter the intake casing flow channel, the high-speed hot air efflux adjacent to the front end of the casing obstructs the droplets near the wall, deflecting their trajectory toward the channel’s mid-region. This results in a higher liquid water content (LWC) in the mid-region of the intake casing, as shown in Figure 17b. Concurrently, droplets in the channel mid-region accelerate streamwise due to the entrainment by high-speed air flow near hot air outlets, while droplets at the top and bottom of the intake casing flow channel exhibit reduced velocities due to the hot air efflux at the casing front end. This effect persists downstream in the intake casing flow channel, causing higher droplet velocities on the left and right sides of Section 1 compared to the top and bottom. Additionally, the inward contraction of the casing channel directs the droplets toward the inner wall, a trajectory confirmed by the streamlines in Figure 16b. Consequently, the LWC near the inner wall of Section 1 becomes notably high, reaching a maximum of 13 g/m³, as depicted in Figure 17c.

After supercooled water droplets approach the struts, they primarily accumulate near the inner support of struts. As the droplets are entrained downstream, a portion impinges on the strut surfaces, while the remainder continues through the passages between them. As previously analyzed, the droplet flow is initially concentrated near the inner wall of the channel before reaching the struts. And, the droplet streamlines depicted in Section 1 indicate that, upon entering the strut region, droplets predominantly impinge on the strut roots, while the remaining droplets flow downstream along the strut airfoils. Consequently, Section 2 exhibits distinct peak regions of droplet velocity and liquid water content (LWC), with these peaks approximately located downstream of the channels between adjacent struts, as illustrated in Figure 16c and Figure 17d. As a result of partial droplet impingement on the struts and their inner/outer support surfaces, the maximum LWC on Section 2 is only 6 g/m³.

As observed in Figure 14 and Figure 15, the velocities and liquid water content (LWC) of supercooled water droplets exhibit non-uniform distributions within the flow channels. This is attributed to two primary factors: the compression effect of the intake geometry and the complex interaction between the main cold air flow and the hot air jets. Pronounced peak regions are evident in Section 1 and Section 2. In contrast, single-component studies [45] often neglect the aforementioned influences in their computational models and boundary conditions, leading to uniform distributions of droplet velocities and LWC in the flow field.

Figure 18 presents the local droplet collection coefficient distributions on the leeward and windward sides of the intake casing. The results reveal that droplets primarily impinge on the rear end of the intake casing leeward side and the front end of the windward side, with significantly more severe impingement on the leeward side. This is because the rear end of the leeward side is located where the main flow channels converge near Section 1. As established in the preceding analysis, the LWC in this vicinity is high, and droplets are directed toward the inner wall, leading to severe impingement with a maximum droplet collection coefficient of 1.8. In contrast, the maximum droplet collection coefficient on the windward side is only 0.22.

Figure 19 depicts the local droplet collection coefficient distributions on the leading edges (center), pressure sides (right), and suction sides (left) of each strut. As can be seen from the figure, there is almost no water droplet impingement at the trailing edges of the five struts. This is due to the “narrow leading and trailing edges with a thicker middle section” profile of the struts, where the middle part effectively shields the trailing edges. Due to the smaller angles of attack of struts 1, 3, and 4 relative to the upstream flow, droplet impingement concentrates on the leading edges near the root, while the larger angles of attack of struts 2 and 5 cause droplets to primarily impinge on their pressure sides. This contrasts with single-strut studies [34,35], where assumed uniform incoming conditions result in impingement across the entire span of the leading edge. Quantitatively, strut 2 exhibits the highest droplet collection coefficient with a peak value of approximately 3.6, followed by strut 1, while strut 5 exhibits the lowest coefficient with a maximum value of only 0.8. Accordingly, in the design of the hot air cavity structure, hot air is routed first through the anti-icing cavities of struts 1 and 2, and finally through the cavity of strut 5.

Figure 20 demonstrates the local droplet collection coefficient distributions on the surfaces of zero-stage guide vanes. The results indicate severe droplet impingement on the surfaces of L9, R2, and R9 guide vanes, corresponding to the upstream flow regions with higher droplet velocities and liquid water content (LWC).

Quantitatively, the maximum local droplet collection coefficient on both struts and zero-stage guide vanes is far greater than 1. This is because, under the combined effects of the air flow compression by the intake ducts and intake casing, the influence of hot air outflow on the flow field, and the interactions between various components, supercooled water droplets tend to accumulate locally. This leads to peak values of water droplet velocity and liquid water content in the flow fields at the accumulation locations, such as upstream of the support plates and zero-stage guide vanes (Figure 16b,c and Figure 17c,d). As a result, the normal velocity of water droplets and the liquid water content at the impingement points on the surfaces of the support plates and guide vanes are much higher than their values at the inlet of the intake ducts [46]; hence, the local water droplet collection efficiency is far greater than 1. This contrasts with the single-component studies [30,31], where local droplet collection coefficients are generally less than 1.

Figure 21 presents two distributions of local droplet collection coefficient for guide vanes L9, R2, and R9: a spanwise distribution along the leading edge stagnation line and a chordwise distribution taken at the spanwise location of the peak coefficient. For the chordwise distribution, the abscissa “+” and “−” represent the vane suction side and pressure side, respectively. As depicted, due to droplet migration toward the inner wall in the convergent flow path, impingement along the vane’s stagnation line occurs primarily on the lower half of the span, near the root, while impingement near the tip is negligible. Along this line, the peak collection coefficient positions for the three vanes occur at 15%, 45%, and 35% of the span, respectively. Figure 21b reveals that, due to the vane angle of attack, the chordwise distribution peaks at the pressure side, with local collection efficiency decreasing gradually from the peak toward either side. Meanwhile, almost no impingement occurs on the suction side. For the guide vane L9, which is most severely impacted, the peak local droplet collection coefficient reaches 3.8. Due to the thinness of the guide vane, the vane body can hardly block water droplets. Therefore, in addition to the leading edge, the water collection coefficient at the trailing edge of the pressure surface also remains at a high level.

5.3. Anti-Icing Characteristics

Figure 22 illustrates the temperature distributions on the anti-icing surfaces of struts and their inner/outer support. The hot air’s flow path dictates the thermal pattern. First, the hot air heats the outer support (at strut tips) before flowing into the anti-icing cavities of struts 1 and 2, then enters the annular air collection chamber at the strut roots to heat the inner support. From the collection chamber, the air is routed successively through the cavities of struts 3, 4, and 5 for heating. The cumulative heat loss that occurs as the hot air travels through the cavity creates a significant thermal gradient, leaving the outer casing, which reaches a maximum temperature of 176 °C, substantially hotter than the inner wall. This thermal gradient is also observed across the struts: the surface temperatures of struts 1 and 2 (heated first) are the highest, while strut 5 (heated last) is the lowest.

Table 3. Average anti-icing surface temperatures of each strut.

Strut	No.1	No.2	No.3	No.4	No.5
Temperature/°C	68.6	54.0	27.3	19.9	14.7

presents the average anti-icing surface temperatures of each strut, showing that the average temperature of strut 1 is 53.9 °C higher than that of strut 5.

Figure 23 presents two temperature distributions for the strut anti-icing surfaces: a spanwise distribution along the leading edge stagnation line, and a chordwise distribution at mid-span. In Figure 23b, the abscissa “+” denotes the pressure side and “−” denotes the suction side. As illustrated in Figure 23a, the anti-icing surface temperatures along the stagnation line gradually increase from the root to the tip for struts 1 and 2, while exhibiting the opposite trend for struts 3, 4, and 5, which is invited by the hot air flow direction within the cavities. For struts 1 and 2, hot air enters the cavities from the tips and flows toward the air collection chamber at the roots, whereas, for struts 3, 4, and 5, hot air flow is reversed, originating from the roots and exiting at the tips. Thus, the peak temperature for struts 1 and 2 is located at their tips, whereas, for struts 3, 4, and 5, it is located at their roots.

The chordwise plot at mid-span (Figure 23b) reveals that, for struts 2, 3, 4, and 5, the temperature peaks at the stagnation point and decreases along both the pressure and suction surfaces toward the trailing edge. Strut 1, however, displays a unique profile on its suction side, where its anti-icing surface temperature first increases then decreases from the leading edge to the trailing edge. This is attributed to two main factors: (1) severe droplet impingement at the leading edge consumes substantial heat for droplet heating and evaporation; (2) the solid structure on the suction side of the strut connects to the outer support and is close to its anti-icing cavity, thus receiving combined heating from both the internal strut cavity and the outer support cavity. Such inter-component thermal interactions are typically neglected in single-strut hot air anti-icing studies.

For struts 3, 4, and 5, the anti-icing surface temperatures at the trailing edges are relatively low, generally below 10 °C. If the aircraft flies at a lower ambient temperature or reduced engine power, the compressor bleed air will be colder than that in this study, potentially reducing the surface temperatures at the trailing edges of these three struts below the freezing point. This creates a significant risk of ice accretion from runback water originating in the leading edge impingement zone. Therefore, implementing additional anti-icing measures for the strut trailing edges is highly advisable.

The hot air exiting from the anti-icing cavities of struts 3 and 5 converges and flows toward the right side of the intake casing, while the hot air from the cavity of strut 4 flows toward the left side. Collectively, these streams heat the anti-icing surfaces of both the windward and leeward sides of the intake casing. Figure 24 depicts the resulting temperature distributions on these surfaces. Since the hot air cavity between the struts and the front air collection chamber of the intake casing is positioned relatively high to the central axis of the intake casing, most of the hot air flows upward due to inertia when entering the front air collection chamber of the intake casing. Thus, the upper front portion of both the windward and leeward sides of the intake casing exhibits higher anti-icing temperatures than the lower portion.

Considering the heat loss along the hot air flow path, one would expect the hot air temperature in the intake casing anti-icing cavity to be lower than that in the strut cavities. However, as observed from Figure 22a and Figure 24, the anti-icing surface temperatures in some areas of the windward and leeward sides of the intake casing are actually higher than those of struts 3, 4, and 5. This can be mainly attributed to two factors: (1) The droplet impingement on the windward and leeward sides of the intake casing is minimal (Figure 18), resulting in less heat from the anti-icing surface being consumed by heating and evaporating water. (2) The solid walls of the intake casing are thinner than those of the struts, presenting a lower thermal resistance to heat conduction.

The rear stream of hot air, illustrated in Figure 6, splits into left and right branches by the hot air inlets at the bottom of the axial flow casing to heat the axial flow casing and zero-stage guide vanes. Figure 25 presents the anti-icing surface temperature of the axial flow casing. As the anti-icing cavity of the axial flow casing is located at its foremost end, the surface temperature gradually decreases along the axial direction. Meanwhile, the temperature is highest at the bottom of the axial flow casing near the inlet, as this region is located closest to the hot air, before significant heat loss occurs along the flow path.

The hot air from the axial flow casing anti-icing cavity is routed into the guide vanes through the inlet ports of their cavities. Consequently, the temperature distribution contour for the anti-icing surfaces of zero-stage guide vanes illustrated in Figure 26 reflects this flow sequence with the black squares on the surface of the zero-stage guide vanes representing the outlet boundaries of their hot-air anti-icing cavity, and the same applies to Figure 27. At the vane tips where the hot air enters, the surface temperatures decrease sequentially according to the order of hot air entering the guide vane anti-icing cavities, from L1 to L9 and from R1 to R9.

Table 4. Average anti-icing surface temperatures of each guide vane.

Guide Vane	Temperature/°C	Guide Vane	Temperature/°C
L1	138.9	R1	145.9
L2	146.8	R2	120.8
L3	135.2	R3	133.8
L4	144.7	R4	145.7
L5	138.4	R5	139.1
L6	155.2	R6	150.1
L7	128.8	R7	129.4
L8	125.4	R8	128.6
L9	102.6	R9	115.2

presents the average anti-icing surface temperatures for each vane, which reveal that the guide vanes L9, R2, and R9 with severe droplet impingement have significantly lower average temperatures. Furthermore, Figure 26 confirms this correlation and indicates that the low-temperature regions on the anti-icing surfaces coincide precisely with the areas of most severe droplet impingement. Despite being at the same spanwise location, guide vane L2 has a much lower impingement and its average surface temperature is consequently 26 °C higher than that of R2. For the guide vanes L3–L7 and R3–R7 on both sides with similarly minimal droplet impingement, the average anti-icing surface temperatures are nearly identical; for example, the average temperatures of vanes L3 and R3 differ by only 1.4 °C.

Figure 27 depicts the temperature distribution of the anti-icing surfaces for zero-stage guide vanes L2 and R2, which reveals several similar patterns: (1) The anti-icing surface temperature is highest at the vane tips, as this is where the hot air first enters the internal cavities. Although the internal hot air flow velocity is low near the leading edge at the tips, heating load from the axial flow casing anti-icing cavity keeps the tip leading edge temperature higher than that at the trailing edge. (2) On surfaces directly backed by an anti-icing cavity, the thin walls allow for more effective heating by the hot air, leading to higher temperatures than adjacent areas. (3) At the vane roots, however, a thicker solid structure between the anti-icing surfaces on both edges and the cavity walls causes the surface temperature to first increase then decrease from the leading to the trailing edge. Quantitatively, the overall surface temperature of vane R2 is lower than that of vane L2. The less heated tip of R2 is mainly due to its longer hot air supply path, resulting in more heat loss and lower temperature, while the colder root is caused by greater heat consumed by droplet impingement.

Previous studies on single guide vanes, such as that by Wang Bo et al. [36], found that the coldest region on the anti-icing surface is located at the leading edge with severe droplet impingement or at the leading edge root. The present study, however, investigates the anti-icing characteristics of the entire intake components accounting for the actual non-uniformity of the flow field and the inter-component thermal effects. The results demonstrate a different finding: the low-temperature areas on the anti-icing surfaces of most guide vanes are located at the trailing edge roots, which has significant implications for design optimization, suggesting that the trailing edge region requires greater attention for anti-icing.

From the temperature distribution on each anti-icing surface, it can be observed that, except for the anti-icing surface near the outlet of the axial flow casing with a temperature of −1 °C, all other anti-icing surfaces are maintained above the freezing point. Since there is essentially no droplet impingement on the anti-icing surface of the axial flow casing, no ice accretion occurs on any anti-icing surface in this case. Consequently, the hot air anti-icing system performs well under this operating condition.

6. Conclusions

This study presents a numerical simulation of hot air anti-icing for the full-annulus intake components of an engine with a real configuration, aiming at its existing anti-icing system. Following the validation of the hot air anti-icing calculation method, the flow field, droplet impingement, and anti-icing characteristics of the intake components under a typical flight condition were obtained through calculations. The main research conclusions are as follows:

(1)

For the struts, droplet impingement primarily concentrates on the root regions of the strut leading edges and the pressure surfaces. The maximum local droplet collection coefficient is 3.6, located on the surface of strut 2. Struts 1 and 2 experience the most severe droplet impingement, while strut 5 has the least impingement amount.

(2)

For the zero-stage guide vanes, droplet impingement mainly concentrates on the vane leading edges and pressure surfaces. The impingement on guide vanes L9, R2, and R9 is relatively severe. The maximum local droplet collection coefficient is 4.2, located at the leading edge of guide vane L9. On the pressure surface side of the vanes, the local droplet collection coefficient gradually decreases from the leading to the trailing edge, while negligible impingement occurs on the suction surfaces.

(3)

The anti-icing characteristics of the intake components are governed by two main factors: cumulative heat loss along the hot air flow path and heat consumption for heating and evaporating the impinging water droplets. Under the studied conditions of this paper, except for the rear end of the axial flow casing, the anti-icing temperatures of all components are maintained above the freezing point, thus preventing ice accretion on all protected surfaces, indicating good overall anti-icing performance.

(4)

For the anti-icing characteristics of the struts, the temperature distributions on the anti-icing surfaces of the five struts are similar, showing a gradual decreasing trend from the leading edge to the trailing edge. The temperature differences between the individual struts are mainly invited by the cumulative heat loss within the anti-icing cavities. The surface temperatures decrease sequentially according to the order in which the hot air flows through them, and the average temperature of the last strut in the heating sequence is 53.9 °C lower than the first.

(5)

For the anti-icing characteristics of a single zero-stage guide vane, the anti-icing surface temperature at the vane root is relatively low. From the perspective of anti-icing characteristics of full-annulus guide vanes, compared with the heat loss along the internal hot air path, the heat consumption for heating and evaporating impinging water droplets has a greater impact on the anti-icing performance. This is evidenced by the result that the low-temperature areas on the anti-icing surfaces of struts all coincide with regions of severe water droplet impingement. For example, due to its higher impingement load, vane R2 has an average temperature 26 °C lower than vane L2.

An analysis of the overall anti-icing characteristics of the intake components provides a more accurate evaluation of the system’s design and offers more valuable guidance for optimizing the anti-icing cavity structure. Under the conditions studied in this paper, the performance of the hot air anti-icing system is satisfactory. However, when experiencing more severe conditions, such as lower ambient temperatures or reduced engine power (when the engine is operating at ground idle), the temperature distribution pattern over the anti-icing surfaces of the intake components remains unaltered, but the absolute temperature values will diminish. Specifically, for the three struts that are the last to be heated, the surface temperatures at their trailing edges could drop below the freezing point. This creates a significant risk of runback ice formation in these areas. Therefore, implementing additional anti-icing protection for the strut trailing edges is strongly recommended.