This study adopts a narrow band model to investigate the cooling and radiation of a vectoring nozzle and to compute the gas spectral characteristic in infrared band. The radiative heat transfer between the hot gas and the wall is considered with an enclosure model. The calculation of film cooling is performed through a cooling effectiveness method. A coupled heat balance equation of heat flux and wall temperature is established on the multilayer structure of the nozzle, including the wall, heat shield, and outer shield, and a Newton-Raphson scheme is taken for solution. Temperature on the expansion part of an experimental nozzle in NASA TN D-1988 is investigated for verification. Another vectoring nozzle with a multirow of film cooling is also investigated. This study shows that the film in the heat shield remarkably cools the convergent part of the nozzle, thereby increasing the temperature on the expansion part of the nozzle. The deflection of the nozzle can change the distribution of the wall temperature and the radiation on the expansion part, which is lower on the deflection side than on the opposite side. The radiation from the nozzle outlet is high, particularly along the deflection direction in the rear hemisphere.

Research on high-performance aeroengines shows that the nozzle is always the most severely heated structure of the engine. The gas temperature of a vectoring nozzle under afterburning condition is higher than 2000 K [_{2}O and CO_{2}, are all strongly spectral dependent, and their infrared radiation is composed of millions of spectral lines.

The waveband model of gas spectral radiation is generally computation intensive. The deflection of the nozzle breaks the axisymmetric distribution of gas flowing parameters and radiation, which also increases the difficulty and calculation of heat transfer analysis. Thus, the accurate coupled calculation of the film-cooling wall temperature and gas infrared radiation is a problem that must be solved in the heat protection optimization of a high-performance aeroengine.

The technology of applying film cooling on the convergent part of a nozzle was first studied on a rocket engine. Reference [

Based on the spectral characteristics of aeroengine gas radiation, [

The vectoring nozzle with a multirow of film cooling investigated in this work is a 0.624 m long axisymmetric nozzle with a 0.8 m diameter afterburning part. The convergent part of the nozzle is 0.184 m long. The heat shield is set on the nozzle, with a gap of 0.006 m from the wall. Three slots of film cooling are applied on the heat shield. The coolant flows through the slots and covers the heat shield surface, thereby forming the adherent film. A part of the coolant directly goes through the end of the gap, rushes to the divergent part of the nozzle, and quickly mixes with the main flow. The outer shield outside the nozzle has a space of 0.1 m from the nozzle wall. The secondary flow goes through the space and conveys some of the heat on outside surface of the nozzle wall. The entire structure of the nozzle is shown in Figure

Geometric model of a vectoring nozzle.

Diagram of three slots film cooling.

The calculation of the wall radiation heat and film-cooling heat transfer in this work is based on the flow field results of the computational fluid dynamics (CFD) software FLUENT. The CFD solution adopts an unstructured grid. We have done a series of calculations based on different grid resolution to get the grid-independent solution. The final grid resolution we adopted is about 107550 grids on

The grids system for CFD solution is not suitable for heat transfer and wall temperature computation, because of the irregular and too dense arrangement of nodes, particularly at the boundary layer of the wall. The density of grid nodes slows down the calculation of gas radiation. Therefore, we reset the grids for radiation calculation. The rearranged grids are divided with the equal space idea on 51 sections. The arrangement of the nodes in each section is shown in Figure

Grid nodes on a cross section.

Grids for heat transfer and wall temperature computation.

An enclosure radiation model is used to calculate the hot gas radiation to the wall. An enclosure is established; it consists of the included hot gases, nozzle wall, inlet surface, and outlet surface. The radiation of each wall unit of the enclosure is calculated. The net radiative heat transfer rate of each unit is given as follows:

On any of the wall cells, the incident radiation

Each solid angle corresponds to a unit surface

The incident radiation at each solid angle is the integral of the gas layer on the incident path, expressed as follows:

Considering the spectrum of gas radiation, the infrared radiation at any direction at the spectrum from 1

For the other waveband outside the infrared waveband, a simplified equation ignoring the gas radiation is given as follows:

A cooling effectiveness model is adopted to calculate the film cooling on the convergent part of the nozzle. The convective heat transfer rate

The convective heat transfer rate of film cooling is given as follows:

In this work, three cooling slots are applied on the heat shield. To calculate the compound cooling effectiveness of the three slots, the cooling effectiveness of multiple slots is calculated based on the result of a single slot. The cooling effectiveness equation of a single slot is given in [

Lumped parameter methods are adopted to calculate the distribution of the wall temperature of all the nozzle structures. A heat balance equation of convective and radiative heat transfer is established on every wall unit as follows:

The calculation of the convective and radiative heat of the wall cells whose inner side is directly heated by gas is discussed in the section above. The convective heat of other wall cells is calculated using the Dittus-Boelter equation. The radiative heat is calculated using the following equation of two envelope surfaces:

Considering any wall cell, the radiative term computed with (

In the iteration of (

The solution we adopt is stepwise and round coupling. First, a set of initial temperatures of the wall cells is assumed. According to these initial temperatures, the heat balance equation is iterated, ignoring the gas radiation. A set of wall temperatures is obtained. Second, the iteration of radiosity is performed according to the wall temperature above. The gas radiative heat transfer rate of the wall cells is generated. Thirdly, according to the newly generated radiative heat, the iteration of the wall temperature is restarted. A set of wall temperatures that consider the gas radiation is obtained and regarded as the result of first round. A new round of iteration will be restarted if temperature difference between two rounds is greater than a minimum limit. Iteration errors of both heat balance and gas radiation get smaller in a new round of iteration.

To verify theoretical and numerical model of this work, a film-cooling aeroengine [

Comparison with [

The measured curve is more gradual in the said reference than in this work. The conductive heat transfer inside the wall is ignored in this work to simplify the calculation. However, high-temperature wall cells transfer heat to the neighboring low-temperature cells, thereby resulting in a gradual distribution of temperature. The difference between the results of the reference and this work is no more than 20%. Therefore, the result of this work can properly reflect the variation trend of the wall temperature under film cooling.

Reference [

Comparison with [

For the vectoring nozzle described in Section

Wall temperature of the heat shield and convergent part.

The temperature distribution on each structure of the nozzle is shown in Figure

Temperature of the entire nozzle structure.

The main effects of vectoring condition on temperature distribution are the uneven distribution of gas parameters after the throat and the occlusion of the throat to the upper wall cells after the throat. The wall temperature distribution of vectoring condition in three circumferential positions is shown in Figure

Temperature distribution at different circumferential angles.

The wall temperature distribution of the nondeflection condition is also obtained in this work. Compared with the deflection of the 20° condition, as shown in Figure

Comparison of 20° deflection and nondeflection conditions.

Figure

Radiosity in infrared and other wavebands on the wall.

Figure _{2}O and CO_{2} radiation at 1.8, 2.7, and 4.3

Spectral radiosity on the outlet surface.

The radiation observed from the rear hemisphere of the nozzle outlet is also computed in this work. Figure

Radiation intensity in all wavebands on the outlet surface.

With the aim of designing the cooling structure design of the AVEN of a high-performance engine, this study established a heat transfer-spectral radiosity coupled heat balance equation model. A 3D all-structure nozzle simulation program of high accuracy was also developed by considering gas radiation heat transfer and film cooling. Our research obtained the following conclusions.

The validation result of this work agrees well with the measured result in a reference, which demonstrates that this work may comprehensively reflect the heat transfer condition in the nozzle.

The convergent part of the axial symmetric vectored nozzle studied in this work is shielded by the heat shield and cooling film. Thus, the wall temperature of this part is relatively low. By contrast, the wall temperature of the divergent part is high and should be the emphasis of the cooling design. The heat shield is the most severely heated structure of the nozzle, a phenomenon that must be considered by the design.

The deflection of the axial symmetric vectored nozzle increases the wall temperature of the divergent part in the opposite direction of deflection and makes it last for a long distance at the downstream, which results in a severely heated area. The deflection also changes the distribution of the directed radiation at the outlet effectively.

There is not conflict of interests for all authors of this paper.

This work is cosponsored by the National Natural Science Foundation of China (51376065, 51176052); Guangdong Key Scientific Project (2013B010405004); Guangdong Province Key Laboratory of Efficient and Clean Energy Utilization (2013A061401005), South China University of Technology; and Key Laboratory of Efficient and Clean Energy Utilization of Guangdong Higher Education Institutes (KLB10004).