Progress of Porous/Lattice Structures Applied in Thermal Management Technology of Aerospace Applications

Abstract

With lightweight, multifunctional, and designable characteristics, porous/lattice structures have started to be used in aerospace applications. Porous/lattice structures applied in the thermal management technology of aerospace vehicles have attracted much attention. In the past few years, many related numerical and experimental investigations on flow, heat transfer, modelling methodology, and manufacturing technology of porous/lattice structures applied in thermal management systems have been widely conducted. This paper lists the investigations and applications of porous/lattice structures applied in thermal management technology from two aspects, i.e., heat transfer enhancement by porous/lattice structures and transpiration cooling. In addition, future developments and challenges based on the previous investigations are analyzed and summarized. With the higher requirements of thermal protection for aerospace applications in the future, thermal management technology based on porous/lattice structures shows good prospects.

1. Introduction

Porous/lattice structures are one kind of material system, which is composed of a regular arrangement and adjustable pore structures. Due to their excellent mechanical, adsorption, penetration and other characteristics, porous/lattice structures show good prospects in engineering applications [1]. In recent years, many fundamental and engineering applications have both been performed on porous/lattice structures and have become the hotpot in heat and mass transfer disciplines. With lightweight, large contacting area, and excellent transporting characteristics, porous/lattice structures show great benefits in thermal management technology for aerospace applications [2,3].

Propulsion technology with high flight speed and high efficiency is required for future aircraft, and advanced thermal management technology is also urgently needed [4]. Thermal protection has become the most crucial aspect in the design of a high-speed aircraft. For example, hypersonic vehicles have attracted much attention in recent decades in military applications. However, the largest challenge for hypersonic vehicles is the thermal protection and related problems of pneumatics, structure, and propulsion caused by overheating [5,6,7,8]. As shown in Figure 1, the largest heat flux regions of a hypersonic vehicle are found in the leading edge, nose zone, and engine interior, where heat flux is usually more than 10⁷ W/m².

Traditional passive cooling methods are difficult to satisfy the requirements of thermal protection for a hypersonic vehicle because the melting points for structure materials are limited [9]. In addition, the problem caused by extremely high thermal load, such as deformations by thermal stress, also limits the use of traditional passive cooling methods [10]. Therefore, the advanced active cooling method is very significant for a hypersonic vehicle, especially in leading-edge regions and the combustor.

With the advantage of lightweight and heat transport characteristics, porous/lattice structures have been introduced to thermal management technology in aerospace applications. According to previous literature, the applications of porous/lattice structures in thermal management technology are mainly grouped into two aspects, i.e., heat transfer enhancement by porous/lattice structures and transpiration cooling.

1.1. Heat Transfer Enhancement by Porous/Lattice Structures

As a new type of lightweight structure, porous/lattice structures can provide large fluid–solid contacting areas and strong flow mixing [11]. The most important applications in thermal management technology are heat transfer enhancement in a cooling channel mounted with porous/lattice structures, such as regenerative cooling in a rocket/scramjet [12,13], turbine blade cooling [14,15,16], and heat exchangers [17,18,19,20].

Many researchers have carried out fundamental investigations in simplified channels and found that, compared with traditional cooling channels, porous/lattice structure-mounted channels offer larger heat transfer enhancement because of the transverse and longitudinal vortices generated [21], which strengthen the mixing of hot and cold flows. Porous/lattice structures with different geometric elements have various heat transfer enhancement and flow characteristics. The geometric structural elements of porous/lattice structures constitute a research interest for researchers in fundamental studies [22]. In addition, the optimization of porous/lattice structure arrangements has also drawn some attention from researchers [23,24].

As an effective active cooling method, cooling channels with porous/lattice structures have started to be used in aerospace devices [25]. For high-speed aircraft in the future, the thermal management of high-temperature components will become a big issue. For the trail edge cooling of a turbine blade, Li et al. [26] numerically investigated the heat transfer of four wedge-shaped channels mounted with different combinations of pin fins, ribs, and Kagome lattices under a strong rotation state. From the results, the cooling efficiency in the trailing edge is greatly improved by Kagome lattice structures. In addition to applications in the active cooling of high-temperature components in engines, the porous/lattice structures are also used in thermal management systems in aerospace devices, such as heat exchangers and heat sinks [18,27].

1.2. Transpiration Cooling

Transpiration cooling is also an important application for porous/lattice structure applications in thermal management technology, which are mainly used in the cooling of aerospace devices, such as turbine blades [28,29,30], combustion chambers [31], and the leading edge [32] of a hypersonic vehicle. Transpiration cooling is a technique where coolant fluid passes through a number of mini-holes from a porous surface to protect the structure from excessive heat damage from external hot gas [33].

In recent years, many researchers [34,35,36] have compared the performance of film cooling and transpiration cooling in terms of overall cooling efficiency and the uniformity of temperature fields. Researchers concluded that the transpiration cooling method can produce better cooling effectiveness and more uniform coolant coverage with less coolant compared with traditional film cooling [37].

Aeroengines output thermal energy of high-temperature gas by turbine blades in the form of mechanical work. In a gas turbine, endwalls of the first-stage vane are directly exposed to high-temperature exhaust gas [38]. To achieve high operation efficiency, a high turbine inlet temperature is required, which also brings high thermal protection requirements for blade cooling. As a new and high-efficiency cooling method, transpiration cooling is introduced to the cooling of turbine blades for advanced areoengines [2,39,40].

Transpiration cooling is also applied in combustion chambers of hypersonic vehicles for thermal protection [41,42]. For a hypersonic vehicle, the aerodynamic thermal environment of the leading edge is severe, and active cooling is needed when it operates at a high Mach number [32]. As an efficient active cooling technology, transpiration cooling has great advantages to improve the cooling efficiency of the leading edge of a hypersonic vehicle [43,44], as shown in Figure 2.

In addition to aerospace applications, some fundamental research works have been conducted to reveal the physical mechanisms of transpiration cooling [3,10,45,46,47,48]. Some researchers [49,50] aimed at finding the optimal porous/lattice structure and revealing the physical process to experimentally improve the cooling efficiency. Other researchers [51,52,53,54,55] developed numerical models to study the flow and heat transfer characteristics of transpiration cooling in porous/lattice structures. Recently, the research works of transpiration cooling have concentrated on high cooling efficiency, improvement of temperature uniformity, and a quantitatively controlled cooling process [56].

In the following parts, the literature on heat transfer enhancement by porous/lattice structures and transpiration cooling is introduced and summarized in detail. In addition, the existing developments and challenges are provided at the end of the paper.

2. Heat Transfer Enhancement by Porous/Lattice Structures

2.1. Theory and Mechanisms

From previous research [57,58], several kinds of complex vortices have been generated, which have benefits in flow mixing when the fluid flows through porous/lattice structures. Convective heat transfer is strengthened with the strengthened mixing of hot and cold flows [59]. For a typical lattice element, there is a horseshoe vortex at the leading edge of the lattice ligaments, a streamwise vortex at the trailing edge, and a counter-rotating longitudinal vortex at the center, as shown in Figure 3. Because of the vortex generation, the local turbulence intensity and flow mixing are both strengthened and then heat transfer is enhanced. However, some research works indicated that the buoyancy effect is weakened because of the porous/lattice structures [60].

2.2. Active Cooling for Scramjet Combustors/Turbine Blades

Aerospace aircraft are developing in the direction of high speed and high efficiency, which also brings higher requirements for thermal management technology [61,62]. Porous/lattice structures have started to be applied in the thermal management of aerospace devices, such as regenerative cooling in a rocket/scramjet [12,63,64,65,66] and cooling of a turbine blade [26,66,67,68,69,70].

For rockets or hypersonic vehicles, effective cooling of a combustor is crucial to ensure safe operation under a complicated heat environment and extremely high heat flux [71]. Yu et al. [12] numerically investigated the heat transfer characteristics of a composite Kagome cored porous/lattice structure used for regenerative cooling of a scramjet. The results indicated that the cooling efficiency of the porous/lattice structure channel was better than that of the conventional channel, although with a large pressure drop penalty. Song et al. [63] numerically investigated flow and heat transfer characteristics of the cooling channel with pyramid lattice sandwich structures in a rocket combustor. They concluded that a regenerative cooling channel with pyramid lattice sandwich structures showed excellent cooling performance. Some other references also confirm the generation cooling effect of a rocket engine via porous/lattice structures [65,66].

For turbine blades, operation efficiency is usually raised by increasing the inlet temperature of turbine blades, and then advanced cooling methods are needed [15]. Many researchers design the internal cooling of a turbine blade using porous/lattice structures [68,70] or design a porous/lattice blade [72]. Xu et al. [68] attempted to optimize the internal cooling channel arranged in the turbine blade manufactured with 3D metal printing technology. The Nusselt number is greatly enhanced with the complex flow path in the lattice/porous blade. Du et al. [72] designed latticework with many sub-channels and numerically studied the effects of the jet nozzle location, shapes, and mass flow ratios on the flow and heat transfer characteristics of the turbine blade. The study provided an important reference for the coupling effect of internal cooling with impingement cooling of a porous/lattice blade, as shown in Figure 4 [73].

In addition, porous/lattice structures are introduced to cool the trailing edge of a turbine blade to provide a bigger heat transfer area and strong flow mixing [26,69,74,75]. Shen et al. [69] experimentally investigated the flow and heat transfer performance of a wedge-shaped cooling channel with a Kagome lattice. The results showed increased heat transfer compared with conventional pin-fin channels at the same porosity, as shown in Figure 5. Saha et al. [75] investigated two types of channels with converging porous/lattice structures on the trailing edge of a turbine blade used for internal cooling with different arrangements. Compared with the previous data from a pin-fin channel, the channel with converging porous/lattice structures presented a higher heat transfer with a larger heat transfer area.

Other related literature studies on porous/lattice structures applied in the active cooling of scramjet combustors/turbine blades are listed in

Table 1. Literature on different applications of porous/lattice structures in aerospace field.

Ref.	Applications	Lattice Type and Geometry	Lattice Material	Coolant	Flow Parameter	Heat Transfer Parameter and Boundary Conditions
[12]	Scramjet combustor	Kagome cored composite lattice structure (d = 2 mm, h = 8 mm, l = 9.8 mm)	C/C composite material	Aviation kerosene	Re = 562–56,234	h = 380–4200 W/(m2·K); T = 1000 K
[64]	Scramjet combustor	Body-centered cubic lattice (d = 0.28–0.82 mm)	Maraging steel, 17-4 PH, and H13	Water	v = 0.5–2.5 m/s	h = 0–55,000W/(m2·K); heat flux = 0.5 MW/m2
[63]	Rocket combustor	Pyramid core lattice sandwich (d = 0.4/0.8 mm, l = 12.2 mm)	1Cr18Ni9Ti	Kerosene	qm = 0.001 kg/s	Nu = 0–110; heat flux = 1.5 MW/m2
[68]	Turbine Blade	Common lattice structure (d = 2 mm)	Nickel-Base superalloy IN718	Air	Re = 6000–12,000	Nu = 110–180; A constant heat flux corresponded the target surface
[72]	Turbine blade	Latticework (l = 224 mm, h = 48 mm)	Aluminium	Cooling air	Re = 44,000	Nu/Nu0 = 0–5; T = 50 ℃
[26]	Trailing edge of turbine blade	Kagome lattice, pin fins, ribs (d = 2.43–5.8 mm, h = 3 mm)	310 stainless steel	Compressible air	Re = 5000	h = 50–170 W/(m2·K); heat flux = 1500 W/m2
[69]	Trailing edge of turbine blade	Kagome lattice, pin fins, ribs (d = 2.43–5.8 mm, h = 3 mm, l = 3.6 mm)	310 stainless steel (0Cr25Ni20)	Air	Re = 5000–15,000	h = 0–150 W/(m2·K); T = 335 K
[74]	Trailing edge of turbine blade	Lattice-matrix structures (e/D = 0.02/0.028, p/e = 8–30)	Stainless steel	Air	Re = 10,000–50,000	Nu/Nu0 = 2.4; T = 120–125 °C
[75]	Trailing edge of turbine blade	Converging lattice structures, pin fins (x/D = 0.6–10)	Low thermal conductivity plastics	Air	Re = 4000–20,000	Nu/Nu =1–4; A time-changing wall temperature

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2.3. Applications in Heat Exchangers and Heat Sinks

A heat exchanger is a type of equipment used to realize heat transport from a hot fluid to a cold fluid, which is also widely used in aerospace applications [76]. It is difficult to further improve the efficiency of the traditional fin heat exchanger [77]. The heat exchanger combined with porous/lattice structures has attracted much attention in recent years [78,79], as shown in Figure 6.

The porous/lattice structures used in heat exchangers usually have two types, i.e., an octet truss porous/lattice structure [81,82,83] or a microporous/lattice structure [84].

The octet truss porous/lattice structure, due to its superior structural characteristics produced by its increased connectivity, has been widely used in multifunctional heat exchangers and electric applications [81,82,83]. Chaudhari [81] experimentally investigated the effective thermal conductivity and wall Nusselt number in heat exchangers with octet truss lattice porous/lattice structures. The results indicated that the octet truss lattice porous/lattice structure is a good selection to bear compressive loads and dissipate heat. Heat and fluid flow characteristics of octet truss lattice porous/lattice structures with different porosities and pore densities were investigated by Ekade et al. [82]. They found that octet truss lattice porous/lattice structures are more suitable for use in heat exchangers compared with stochastic foams.

Micro-porous/lattice structures draw more attention as a kind of new structural material because of their strengths in lightweight and high structure stability [84,85]. Maloney et al. [85] experimentally studied the heat transfer performance of a heat exchanger with a three-dimensional micro-porous/lattice structure in terms of thermal conductance per unit of volume. The results indicated the multifunctional capability of micro-porous/lattice structures for load bearing and energy absorptions.

Some researchers attempted to apply the porous/lattice structure in heat sinks to improve the cooling efficiency [27,86,87,88,89]. Dixit et al. [27] numerically compared several kinds of porous/lattice structures regarding their convection flow at a low Reynolds number and in constant wall temperature conditions. They found that the body-centered-cubic truss, simple-cubic plate, and Kelvin and Octet lattice cells provided better heat transfer than microchannels or channels with open-cell foam elements. Wang et al. [86] numerically investigated the flow and heat transfer characteristics of a cubic body-centered-cubic pin fin heat sink. They found the usage of the combination of conventional pin fin and porous/lattice structure brought a more than 140% improvement in thermal-hydraulic performance.

2.4. Manufacture of Porous/Lattice Structures Cooling Channel

Porous/lattice structure channels are mainly grouped into two types: Metal porous/lattice structures [90] and plastic porous/lattice structures [91]. The selection of lattice/porous material is important in the heat transfer process and, consequently, makes a difference in heat transfer performance. As for the metal lattice, complex metal porous/lattice structures can provide good heat transfer performance because of their high heat conduction coefficient and strong designability [78,92]. Metal porous/lattice structures have been widely applied in aerospace in the main components and related assisting components, such as heat exchangers. Furthermore, some nonmetal porous/lattice materials are also investigated [93], such as composite materials. In addition to metal and nonmetal porous/lattice structures, plastic materials are also used to fabricate porous/lattice structures, which have good capability in shock absorption [91].

The manufacturing methods of porous/lattice structures usually include selective laser melting, additive manufacturing, sheet folding and interweaving, and chemical vapor infiltration. Yun et al. [64] manufactured a series of face-centered cubic lattice channels by additive manufacturing and analyzed their flow and heat transfer characteristics at different porosities and inlet velocities. The effects of different structure materials were compared and it was found that the performance of the H13 steel channel was better than those of maraging steel and 17-4 PH steel channels. Ho et al. [80] fabricated two novel porous/lattice heat exchangers via additive manufacturing, and the thermohydraulic performance of the heat exchangers was experimentally analyzed. The results indicated that with a smaller cell size, the heat exchanger has higher overall thermal conductivity and air-side heat transfer coefficients. Ho et al. [94] produced four structured porous/lattice structures with the same porosity but of different unit element sizes via selective laser melting to study the thermohydraulic properties in terms of the permeability, inertia coefficient, and Nusselt number and provided a theoretical reference for enhancing single-phase forced-convection cooling. Jin et al. [95] fabricated metallic lattices with different punching locations to investigate the effects of a dimensionless punching location shift (s/d) on flow and heat transfer characteristics via the sheet folding method. The results indicated that the heat transfer capability of the pyramidal lattice (s/d = 0) was superior to the lattice with a quarter punching location shift (s/d = 0.25), which was followed by the X-lattice (s/d = 1). Wei et al. [96] manufactured a lightweight C/SiC pyramidal core porous/lattice structure panel via interweaving and the chemical vapor infiltration method. Combining experiments with simulations, the equivalent thermal conductivity of the structure was obtained and indicated the good heat transfer performance of the C/SiC materials.

2.5. Investigations of Porous/Lattice Structure Element

There are various element types of porous/lattice structures (shown in Figure 7). When the fluid flows through porous/lattice structures, different vortices are generated, which affects the flow structures and turbulence intensity [97].

In the past few years, several common porous/lattice structures have been investigated by researchers, such as octet truss lattice, face-centered cubic, body-centered cubic, micro-lattice, pyramid lattice, Kagome lattice, X-lattice, vertical lattices, tetrahedral lattices, slanted lattices, graded lattice, and composite lattice [19,21,22,23,67,69,98,99,100,101,102,103,104,105,106,107,108].

The effects of different lattice elements have been numerically investigated by researchers [21,101,106]. Shen et al. [21] studied the local and overall flow and heat transfer characteristics of the single-layered Kagome and wire-woven bulk Kagome lattice by a verified SST numerical model. They found the area-averaged Nusselt number on the ligaments of single-layered Kagome was lower than that of wire-woven bulk Kagome, which resulted from more high-momentum vortices and higher turbulent kinetic energy near the endwall as a result of the Kagome panel. Downing et al. [101] numerically analyzed the flow and heat transfer characteristics to optimize the manufacturing thermal process. The results provided a great reference for the effects of local geometry and topology on temperature field evolution in lattice structures during metal additive manufacturing. Yun et al. [106] numerically investigated the thermos-fluid-structural characteristics of the increase-type graded, V-type graded, and W-type graded lattice channels. The results provided strong evidence for heat transfer enhancement for graded porous/lattice structures.

Moreover, some researchers carried out experiments to analyze the effect of the porous/lattice elements [58,105,108]. The overall heat transfer performance of a vertical tube under a low flow rate and high heat flux with a body-centered cubic porous/lattice structure was investigated by Shi et al. [58] to suppress the heat transfer deterioration. Supercritical CO₂ is used in the experiments. Liang et al. [105] experimentally compared the thermo-fluid behaviors of a staggered pin fin array, a Kagome lattice array, and a body-centered cubic lattice array in a rectangular channel. The results indicated that the endwall-averaged Nusselt number of the body-centered cubic and Kagome lattices were higher than conventional pin fins but had similar heat transfer characteristics. Bai et al. [108] conducted a systematic experiment to obtain the heat transfer performance of five lattice core structures, i.e., vertical lattices, tetrahedral lattices, slanted lattices, pyramidal lattices, and Kagome lattices. Based on the experimental results, they finally proposed a novel lattice core structure named after the windward bend structure, with the lattices bent in the windward direction and arranged in a staggered pattern.

Some researchers combined porous/lattice structures with other heat transfer enhancement elements [67,69,102]. Li et al. [67] introduced dimples, protrusions, and pin fins into an X-lattice-cored sandwich panel downstream. The results indicated that the appropriate combination of the X-lattice and a certain element is beneficial for the overall heat transfer enhancement of the sandwich panel. Shen et al. [69] numerically compared the heat transfer capability of pin fins with that of Kagome porous/lattice structures on the trailing edge of a turbine blade. They found the Kagome porous/lattice structures can increase the overall Nusselt numbers but result in a similar pressure loss compared with the traditional cooling arrangements. Ma et al. [102] numerically investigated the forced convection heat transfer in a new sandwich panel mounted with a pyramidal lattice and plate fins. The thermal performances of different kinds of sandwich panels are compared. The results indicated that the combination of pin fins and pyramidal lattice produced a larger overall Nusselt number and better heat dissipation performance.

Overall, the octet truss lattice and the micro-lattice are suitable for heat exchangers or heat sinks because of the excellent structural characteristics and heat transporting ability [103]. Because of their higher bearing capability, the body-centered cubic (BCC) structure and face-centered cubic lattice (FCC) structure are widely used in aerospace fields for multifunctional applications such as load bearing, vibration isolation, and thermal protection. Literatures on different elements and related parameters of porous/lattice structures are listed in

Table 2. Literature on different elements and related parameters of porous/lattice structures.

Ref.	Lattice Type and Geometry	Lattice Material	Coolant	Flow Parameter	Heat Transfer Parameter and Boundary Conditions
[21]	Single-layered Kagome and wire-woven bulk Kagome cores sandwich (d = 1.0/1.68 mm, l = 12.73 mm, h = 13 mm)	Copper-2% Beryllium (Be2Cu) alloy	Incompressible fluid with constant thermophysical properties	Re = 3995–8710	Nu = 50–200; heat flux = 4000 W/m2
[22]	X-type metallic lattice cored sandwich panel, tetrahedral lattice cored sandwich panel (w = 2.16 mm, l = 12 mm, h = 12 mm)	AISI 304 stainless steel	Air	Re = 2165‒6043	Nu = 0–500; heat flux = 4088‒8529 W/m2
[58]	Body-centered cubic lattice (h < 4.5 mm)	316L stainless steel	Supercritical CO2	mass flux = 130–419 g/(m2·s)	Nu = 100–400; heat flux = 41.94 kW/m2
[67]	X-lattice-cored sandwich panels with pin fins, dimples or protrusions (l = 12 mm, w = 12 mm, h = 9.66 mm)	AISI 304 stainless steel	Air	Re = 3100–5700	Nu = 40–260; heat flux = 9882.6 W/m2
[69]	Kagome lattice structures, pin fins lattice structures (d = 3.52/3.28/2.43/5.8/4.25/2.5 mm, h = 3 mm, w = 30 mm)	ASTM type 310 stainless steel (0Cr25Ni20)	Air	Re = 5000–15,000	h = 0–150 W/(m2·K); heat flux = 1500 W/m2
[98]	A new lattice with non-uniform wall roughness (p/D = 1.12)	Stainless steel	Air	Re = 38,754	Nu = 210–400; Tin = 47 ℃
[99]	Composite lattice core sandwich structures (l = 10 mm, w = 10 mm, h = 1 mm)	CF-reinforced resin matrix composite (CFRP)	Incompressible fluid with constant thermophysical properties at 300 K	Re = 0–100,000	Nu = 10–1000; heat flux = 10 kW/m2
[100]	Multi-layered lattice structures (d = 2 mm, l = 17.3 mm)	Aluminium	Air	v = 5.4–11 m/s	h = 90–220 W/(m2·K); T = 350 K
[102]	Plate fins or/and pyramidal lattice (l = 12 mm, h = 9.64 mm, w = 12 mm)	A kind of solid with thermal conductivity = 16.2 W/(m·K)	Air	Re = 3100–5700	Nu = 83.31–196.27; heat flux = 9882.6 W/m2
[105]	Staggered pin fin array, Kagome lattice array, body centered cubic lattice array (d = 7.4/4/3.4 mm, l = 20 mm, h = 15 mm)	Acrylic plastics	Compressed air	Re = 5000–20,000	Nu = 20–55; T = 293 K
[106]	Increase-type graded, V-type graded, W-type graded lattice (d = 0.3–0.57 mm)	17-4 PH steel	Water	v = 0.1–0.5 m/s	h = 5000–14,000 W/(m2·K); heat flux = 300 kW/m2
[107]	Composite sandwich structure with lattice truss cores (d = 1/1.5/2.5/3 mm, h = 9/10/14/16 mm)	Carbon-fiber-reinforced resin matrix composites (T700/3234)	A specific fluid with T = 300 K	v = 5 m/s	h = 161.68–171.13 W/(m2·K); heat flux = 10 kW/m2
[108]	Vertical lattices, slanted lattices, Kagome lattices, tetrahedral lattices and pyramidal lattices (d = 0.35 mm)	Metal foam	Air	v = 1–12 m/s	h = 0–660 W/(m2·K); An equal pumping power
[109]	A new lattice with nonuniform wall roughness (e = 2.8 mm, p/e = 4–15)	Stainless steel	Air	Re = 2000–22,000	Nu = 10–105; heat flux = 1390 W/m2

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3. Transpiration Cooling

3.1. Theory and Mechanism

Transpiration cooling is an effective active cooling method that causes the coolant to flow into the micro skeleton material of porous/lattice structures and consequently generate convective heat transfer [110]. At the same time, a thin film is formed covering the solid surface of the used piece when the coolant flow is ejected, which can isolate the protected surfaces from the high-temperature mainstream [111,112,113], as shown in Figure 8. Transpiration cooling can improve the cooling efficiency using a limited coolant and provide a large amount of contact surface for the solid surfaces and coolant flows [114]. Recently, some researchers have concentrated on the research of transpiration cooling in terms of cooling efficiency [37,115]. Compared with traditional film cooling, transpiration cooling has the advantages of more uniform coolant coverage, less coolant consumption, and a larger solid–fluid contact area.

3.2. Experimental Study

Experimental investigations on transpiration cooling can be divided into two groups. One group is based on porous/lattice plates to perform a fundamental study of transpiration cooling [10,35,45,115,116]. The other group is application study, including transpiration cooling in turbine blades [117,118,119,120], nose cones [33,121], combustion chambers [122], and leading regions [123].

Based on sintered metal porous/lattice plate, researchers have conducted a series of investigations on transpiration cooling [10,35,45,115,116]. These experiments were mainly conducted in a heated wind tunnel, and the coolant was supplied by an air compressor. Zheng et al. [35], using the selective laser metal sintering additive manufacturing technology, fabricated different kinds of lattice plates for transpiration cooling investigations. They experimentally analyzed the effects of geometry parameters on heat transfer performance, including five different types of porous media, three different coolant mass flow rates, and four different mainstream temperatures. Jiang et al. [115] proposed a combination of transpiration cooling and film cooling based on the leading edge. It was found that cooling efficiency increased by 25.7% for standard transpiration cooling and by 37.9% for combined cooling. Huang et al. [116] investigated the effects of the particle diameter of the sintered porous/lattice structure and coolant injection ratio on the transpiration cooling efficiency in a supersonic wind tunnel system in which the air was compressed to 0.55 MPa. The temperature distribution of the porous/lattice structure surface was captured by an IR camera.

Some researchers carried out experiments based on turbine blades to improve cooling efficiency [117,118,119,120]. Kim et al. [118] investigated micro cooling for s turbine blade by a DPSS laser and a high-speed CCD camera imaging system. They found transpiration cooling had a relatively stable boundary layer and verified it by simulation methods. Using steam as the coolant, Kumar et al. [119] performed an evaluation of the performance enhancement of a combined cycle based on transpiration cooling of gas turbine blades. The results indicated that steam was the superior coolant compared to air, and a gas/steam combined cycle could be an alternative adoption. Kim et al. [120] performed experiments on a single C3X blade with a multiple-hole array in a high-temperature subsonic wind tunnel. The surface temperature of the blade was measured, and the overall cooling effectiveness was analyzed. The results indicated that the adoption of transpiration cooling brought nearly one-quarter of cooling effectiveness improvement compared with internal cooling (shown in Figure 9).

Transpiration cooling becomes necessary in some components, such as nose cones [33,121], combustion chambers [122], and leading regions [123], because the extremely high heat flux is generated during high-speed flights. Wang et al. [33] investigated the transpiration cooling for a wedge-shaped nose cone with an unequal-thickness porous wall using liquid water as a coolant in a heated gas wind tunnel. The results indicated that the arrangement for the unequal-thickness walled nose cone can effectively solve the key issue of the cooling stagnation point. For transpiration cooling of the nose cone, Wu et al. [121] adopted two nose cone specimens, namely, “uniform porosity layout” and “gradient porosity layout”, to carry out experiments. They found that using a “gradient porosity layout” could reduce the required coolant injection pressure (shown in Figure 10). The transpiration cooling efficiency in an annular slinger combustor was investigated by Zhang et al. [122]. The wall temperature and cooling effect of the combustor were observed to provide a reference of flow structures and heat transfer performance. Shen et al. [123] experimentally investigated the transpiration cooling of the leading edge in an arc-heated wind tunnel. An infrared thermal imaging system was used to capture surface temperature distributions using coolant water. They found interesting phenomena such as ice formation in a high enthalpy environment.

The effects of coolants are also evident, for example, the use of steam as a coolant is more effective than air [37]. Many researchers concentrated on the effects of different coolants to search for optimal cooling performance [124,125]. Qian et al. [125] used hydrogel as a coolant and experimentally compared the cooling characteristics using hydrogel and water as coolants, respectively. The results indicated that hydrogel can provide a considerable cooling effect and was superior for prolonging service time. In addition, He et al. [126] added propylene glycol to water to investigate the cooling effect. The results indicated that adding propylene glycol to water was an effective way to ease the unfavorable matters existing in transpiration cooling with liquid water, such as the stability of temperature distribution and the uniformity of coolant coverage. Literatures on different applications used in transpiration cooling are listed in

Table 3. Literature on different applications used in transpiration cooling.

Ref.	Applications	Plate Material	Coolant	Mainstream
[10]	Sintered porous flat plates	Stainless steel or bronze	Air	Dry air supplied by a blower (30 m/s, 100 °C)
[46]	Sintered woven wire mesh structures	Stainless steel	Cooling air (20.5–22.3 °C)	Air (130–150 kg/h, 100–130 °C)
[115]	Leading edge	Stainless steel (1Cr18Ni9Ti)	Room temperature dry air	Air (Ma2.8, 398.15 K)
[116]	Sintered porous plates	Bronze	Liquid water (293.2 K)	Hot air (65 m/s, 800 K)
[117]	C3X blades	Stainless steel (SUS304)	Cooling air	Dry air (3197 m3/h, heated by three electrical heaters)
[121]	Nose cone	316L alloy powder	Cooling air and liquid water (20 °C)	Air (20 m/s, 100 °C)
[122]	Annular Slinger Combustor	GH3044	Fresh air	Air (7.3 kg/s and 742 K)
[125]	A porous flat plate specimen	Nickel-based powders (Ni 73.46%, Cr 17.3%, Fe 7.5%, Si 1.7%, and C 0.04%)	Solid hydrogel	Air (523 K and 693 K)
[126]	A sintered porous plate and a solid frame	Nickel-based super alloy powders (73.46%Ni, 17.3%Cr, 7.5%Fe, 1.7%Si and 0.04%C)	Propylene glycol aqueous	Air (Re12000, 523 K)

.

3.3. Numerical Study

Many numerical simulations of transpiration cooling have also been performed by researchers, which are mainly grouped into single-phase transpiration cooling and phase-change transpiration cooling [123]. For single-phase transpiration cooling, different kinds of turbulence models are adopted, such as the Spalart–Allmaras turbulence model [43,127], the k-ε turbulence model [128,129,130,131,132,133], and the k-ω SST turbulence model [134,135,136,137].

The Spalart–Allmaras turbulence model is specifically designed for aerospace applications involving bounded flow on walls, which has shown excellent results for boundary layers subjected to adverse pressure gradients [43,127]. He et al. [43] proposed two optimization strategies and developed five locally enhanced transpiration cooling designs after analyzing the interaction performances in a three-dimensional hypersonic inlet using the Spalart–Allmaras model. Huang et al. [127] numerically investigated transpiration cooling for a sintered porous strut with different strut structures, material properties, and coolant conditions using the Spalart–Allmaras model. The results indicated that increasing the coolant blowing ratio could produce an increase in the retention time of a mixture of steam and injected coolant.

Apart from the one-equation turbulence model, two-equation models, such as the k-ε turbulence model [128,129,130,131,132,133] and the k-ω SST turbulence model [134,135,136,137], are also used in simulations of transpiration cooling. Jiang et al. [129] compared the turbulent velocity and thermal characteristics of the main flow in a rectangular channel without and with transpiration cooling using the k-ε SST model. The results indicated that transpiration cooling could produce a thicker boundary layer and less wall skin friction. Kilic [131] studied the influence of the Reynolds number of hot gas, the inlet temperature of the air, and the mass flow rate of water on the temperature distribution of a local wall and the cooling effectiveness of a porous flat plate using the k-ε RNG model. It was found that with the increased Reynolds number, the surface temperature increased and the cooling effectiveness of the porous plate and the efficiency of the system decreased. Bellettre et al. [133] examined the liquid transpiration cooling effect of a porous plate using the k-ε RNG model and confirmed the evaporation rates calculated by semi-empirical relations. The related results can be applied in the regenerative cooling of rocket combustors and other internal cooling of high-temperature components.

Yang et al. [134] investigated the phenomenon of plugging pores for transpiration cooling using the k-ω SST model. They found that, although the overall plugging ratio was a dominant parameter for the cooling effectiveness, this single parameter was not enough to improve the cooling effectiveness for all locations but did provide a quantitative understanding of the random plugging on the specific transpiration cooling configuration. Ding et al. [135] carried out investigations on heat transfer performances of a porous matrix using a combination of transpiration and film cooling using the k-ω SST model. They systematically investigated the downstream film cooling effect derived by upstream transpiration cooling using gaseous Nitrogen as the coolant. Shen et al. [136] used the k-ω SST model to analyze a combinational opposing jet and platelet transpiration cooling nose-tip. Compared with only using the opposing jet, they found that using the combinational opposing jet and platelet transpiration cooling could result in a reduction of peak heat flux at more than 6.6% with less coolant consumption.

Some researchers conducted simulations based on the coolant phase-change process, which fully exploits the latent heat of vaporization occurring in the phase change of the coolant. Two kinds of phase-change models are used, i.e., the semi-mixing model [138,139,140,141] and the Local Thermal non-Equilibrium Two-Phase Mixture Model [51,142].

In 2013, He et al. [138] studied the influences of the coolant injection rate and external heat flux on temperature distributions using a numerical method validated by experiments. Based on the theoretical results, they [139] investigated thermal protection under extremely high heat flux and estimated an approach to analyzing the maximum heat flux afforded and minimal coolant required for the desired conditions of transpiration cooling in 2014. Recently, they [140] suggested using semi-mixing to investigate the reliability and stability of transpiration cooling in changeable and complicated cases. Dong et al. [141] used the semi-mixing model to analyze transpiration cooling with the coolant phase change and found it can overcome the difficulties of tracking the phase-change interface and avoid calculation mistakes, which was validated by experiments.

The Local Thermal non-Equilibrium Two-Phase Mixture Model is also adopted by many researchers to describe the physical process of phase change in liquid coolants [51,142]. Yang et al. [51] investigated the mechanism of transpiration cooling and studied the effects of the coolant mass flow rate and various coolants. They found low-density and high-specific-heat coolants could generate a thicker film and produce a better cooling effect. Shi et al. [142] studied the influence of thermal conductivity, sphere diameter, and porosity on the temperature and saturation distributions within the matrix and numerically discussed the effect of hot surface pressure.

Recently, multi-discipline research methods have been proposed to improve transpiration cooling, such as biology [143,144]. Huang et al. [143] designed self-pumping transpiration cooling based on tree-like micro-channels. The results indicated the heated surface was efficiently cooled by the system, and upon increasing the heat flux, the coolant mass flow rate self-adaptively increased. Furthermore, Huang et al. [144] used a biomimetic non-smooth surface, which was inspired by earthworms, to compare the cooling efficiency of porous plates with three types of shapes. The results indicated that the non-smooth surface inspired by earthworms has important significance in heat transfer enhancement within porous/lattice materials. Literatures on different numerical models used in transpiration cooling are listed in

Table 4. Literature on different numerical models used in transpiration cooling.

Ref.	Applications	Plate Material	Coolant	Numerical Model
[41]	Rocket thrust chambers	Composite carbon/carbon materials	Air, argon and helium	Darcy–Brinkman–Forchheimer model, local thermal equilibrium model
[43]	Three-dimensional hypersonic inlet	High temperature alloy Inconel-600	Purified water	Spalart–Allmaras model
[51]	Combustion chamber	Stainless steel	Methane	Local Thermal Non-Equilibrium Model
[127]	Combustor	Stainless steel	Methane	Spalart–Allmaras model
[129]	A rectangular channel	Sintered bronze	Air	k-ε Standard model, two-layer k-ε model
[130]	Nose zone	Stainless steel	Air or other gases (N2, He, Ar, CO2)	k-ε Standard model, k-ε RNG model, k-ω SST model
[131]	A porous plate	Porous plate with a porosity of 0.4	Water	k-ε RNG model
[132]	A porous plate	Bakelite	Compressed dry air	k-ε Standard model
[134]	Hot sectioncomponents	A porous metal plate with multiple rows of straight holes	Air	k-ω SST model
[135]	Leading edge and entire structure of hypersonic vehicles	single porous matrix and binary porous matrixes	Gaseous nitrogen	k-ω SST model
[136]	Nose-tip	Bonding thin metal platelet with a limited number of enlarged transpiration orifices	Air	k-ω SST model
[137]	A series of porous metal plates	Porous metal plate with large numbers of straight cylindrical holes	Air	k-ω SST model
[139]	An infinite porous plate	Porous plate with specific thickness, porosity, sphere diameter, and thermal conductivity	Water and vapor	Local thermal equilibrium model
[141]	A porous plate	Porous plate with specific thermal conductivity and permeability	Liquid water	Semi-mixing model
[142]	A porous matrix	Porous matrix with specific thickness	Pure water	Two-phase mixture model with the local thermal nonequilibrium model
[145]	A porous plate	Porous plate with constant physical properties	Hot flow with constant thermal physical properties and density	Local thermal equilibrium model
[146]	A porous material	A cooled porous ceramic matrix composite material	Air	k-ω SST turbulence model
[147]	A turbulence channel	Metal plate composed of Fe, Cr, Ni, Si, Mn, and C	Cold air	Darcy–Forchheimer model, local non-equilibrium thermal mode
[148]	A heated copper plate	Copper	Slurry and nanofluid	k-ε Standard model and k-ω SST model

.

4. Developments and Challenges

4.1. Heat Transfer Enhancement by Porous/Lattice Structures

(1)

For the applications of porous/lattice structures in scramjet/rocket engines, the investigations are still limited. The selection of the coolant is also limited by a relatively low heat flux. Most researchers select water or kerosene as coolants and the applied heat flux ranges from 0.5 to 1.5 MW/m², which is lower than the actual thermal environment.

(2)

For the applications of porous/lattice structures on the trailing edge of a blade, the related investigations are almost all numerical calculations. The blade wall temperature is close to 335 K with a coolant temperature set at room temperature, as shown in Table 1. These parameters are far from the real thermal environment of the trailing edge of turbine blades. The effect of thermal-physical properties changing with temperature is ignored. For investigations of a whole blade with a latticework design, these studies were carried out at a temperature difference of approximately 20 K, and high-temperature effects are also ignored. In addition, reliable experimental data are also needed in this field.

(3)

For heat exchangers and sinks, two lattice types, i.e., octet truss lattice and micro-lattice, are mainly used to obtain larger heat transfer areas. However, the current research on heat exchangers and sinks is mostly limited to the regular shape with low heat flux. Determining how to effectively dissipate heat in a high-temperature environment and with limited space, such as in aerospace applications, still needs further exploration.

(4)

Although manufacturing technology has developed significantly in recent years, additive manufacturing technology has limited applications in porous/lattice metal materials. Determining how to control the porosity and uniformity of the porous/lattice structures is still a big problem for additive manufacturing technology. Therefore, the investigations of porous/lattice structures in regenerative cooling and cooling of a turbine blade are still at the theoretical level, and more investigations are needed before its applications in practice.

(5)

Investigations on the heat transfer characteristics of porous/lattice structures mounting a cooling channel are mainly numerical calculations. The experimental research works are limited, especially for high-temperature and high-pressure-flow conditions, such as scramjet/rocket combustors and turbine blades.

(6)

The porous/lattice structures are proposed to achieve heat transfer enhancement. For this kind of material, heat transfer enhancement, structure strength, and weight are contradictory in practice. Therefore, it is necessary to conduct a comprehensive evaluation of the performance of all aspects when designing the structure to meet the requirements of use under different working conditions.

(7)

Highly efficient and accurate numerical models dealing with flow and heat transfer passing through porous/lattice structures are needed. Porous/lattice structure configuration optimization technology that considers multi-scale and multi-physical field effects needs to be developed.

4.2. Transpiration Cooling

As a new active cooling technology, transpiration cooling has developed rapidly in recent years and will face challenges in the future.

For experimental investigations:

(1)

High-temperature experiments are hard to find in the literature, but they are necessary when transpiration cooling is applied in high-temperature components, such as combustors, the leading edge of a hypersonic vehicle, and turbine blades. The high-temperature field of porous media is difficult to capture because of the weakness of the high-temperature measurement technique. The flow fields of the porous structure measured by experiments are hardly found, which prevents the study of the physical mechanism of transpiration cooling from an experimental perspective.

(2)

Transpiration cooling can be used for blades, leading edges, nose zones, combustion chambers, etc., but the existing experimental conditions find it difficult to meet the high-temperature environment and manufacture precision components, so many experiments are carried out based on a simplified flat plate structure made of stainless steel or bronze. In these experiments, the temperature of the stream mainly ranges from 373–800 K and the flow velocity mainly ranges from 20–65 m/s. Only in some investigations into the transpiration cooling of the leading edge of a hypersonic vehicle did the main steam total temperature reach 2310 K and the main steam velocity reach Ma = 4.2.

(3)

For experimental studies, the coolants used for transpiration cooling are primarily air, water, solid hydrogel, and propylene glycol aqueous. The materials of porous/lattice structures are primarily plastic and metal. Apart from metal and plastic porous/lattice structures, there are also certain materials with a high melting point and good thermal conductivity used for transpiration cooling. In recent years, to meet the extremely high-temperature conditions, the porous materials used in the experimental research of transpiration cooling have been developed with composite materials such as C/C composite material in order to obtain better cooling efficiency.

For numerical investigations:

(1)

For the numerical study of single-phase transpiration cooling, the porous/lattice structures region is often simplified as a fluid zone with resistance and source items. The simplified model cannot accurately describe the flow field and temperature field in the porous zone. When geometric details of the porous/lattice structures are considered in calculations, large computational efforts are needed to deal with the physical model. Therefore, a more accurate model of porous/lattice needs to be developed.

(2)

The development of phase-change models of transpiration cooling is also limited, and the existing phase-change models require water as the coolant. With the extremely high thermal protection demand in aerospace applications, phase-change transpiration cooling has more potential to be used. The development of phase-change models should be coupled with a single-phase porous/lattice structure model to provide highly efficient and accurate predictions.