3.3.1 Influence of an adjustable nozzle area on the primary engine

The influence of a cooled 2-D TV nozzle on the engine can be analysed from two aspects, which are the nozzle flow area and nozzle cooling. The first factor is analysed in the following paragraphs.

When the nozzle is working in the choked state, according to the flow equation, the nozzle throat area ${A_{throat}}$ determines the mass flow of the gas through the nozzle ${m_g}$ as follows:

(8) \begin{equation}{m_g} = \sqrt {\frac{{{\gamma _g}}}{{{R_{\rm{g}}}}}{{\left(\frac{2}{{{\gamma _g}+1}}\right)}^{\frac{{{\gamma _g}+1}}{{{\gamma _{_g}} - 1}}}}} \frac{{P_{throat}^*{A_{throat}}}}{{\sqrt {T_{throat}^{\ast}} }}q(Ma)\end{equation}

where, $q(Ma)=1$ for the flow at the nozzle throat section is sonic, ${\gamma _g}$ is the specific heat ratio of the exhaust gas, and ${R_{\rm{g}}}$ is the gas constant of the exhaust gas.

Under this circumstance, reducing ${A_{throat}}$ leads to a decrease of the engine air flow. This interferes with the flux continuity of the engine and finally cause a deviation of the engine’s operating balance.

Figure 7.

Fan surge margin variation with nozzle throat area decrease.

When the nozzle is working in the unchoked state, the Mach numbers at the nozzle throat section and the exit do not reach 1, and the static pressure at the nozzle exit ${P_9}$ equals the ambient pressure ${P_0}$ . Under this circumstance, reducing ${A_9}$ improves the gas expansion. This leads to an increase of the total pressure at the nozzle inlet $P_7^*$ ; hence, this influences the engine operating state.

For twin-spool aeroengines that have a by-pass located behind the fan, the increase of $P_7^*$ (or the total pressure at the mixer outlet $P_6^*$ ) caused by the diminution of the nozzle throat area influences the engine operating state from two aspects. The first is that the increase of the total pressure behind the low pressure turbine (LPT) causes its pressure ratio to decrease, and the low pressure rotor (LPR) decelerates because the LPT is not producing enough power. At this moment, the engine control system, usually conforming to the control schedule of maintaining the LPR speed, increases the burner fuel supply. As a result, the LPR speed remains stable while the high pressure rotor (HPR) works at a higher speed and the high pressure compressor (HPC) draws in more air. Consequently, the fan operating point on the characteristic map moves further from the surge boundary along the constant-speed line. From the second aspect, the increased back pressure of the by-pass blocks the air flow of the fan, under the condition that the LPR speed remains unchanged. As a result, the fan operating point moves toward the surge boundary, which may improve the engine performance to some small extent, but also impose a threat on the aircraft safety. The consequent variation of the fan operating point relates to these two aspects and mainly depends on the BPR. For engines that have relatively small BPRs, the first factor dominates when the nozzle throat diminishes, while for engines that have larger BPRs, the diminution of the nozzle throat causes the fan operating line to move nearer to the surge boundary^{(Reference Hamed and Vogiatzis49)}. In this paper, based on a 0-D component-level simulation model of a mixed-exhaust engine with a designed BPR that is approximately 0.7, the fan surge margin variation with nozzle throat diminution under several typical flight conditions are estimated (Fig. 7). The results show that reduction of the nozzle throat area deteriorates the fan operating state. In summary, properly controlling the nozzle throat area is the key to maintaining the engine working state.

According to the previous section, deflecting the 2-D TV nozzle causes the skewing of the nozzle throat and the diminution of its area from ${A_8}$ to ${A_{8e}}$ if one of the divergent flap angles turns negative. For this reason, in order to maintain the engine working condition, ensuring the nozzle throat area remains constant when the nozzle deflects is a key consideration. Because the influence of non-isentropic factors and the cooling air, the real nozzle throat flow area is always less than ${A_{8e}}$ ; thus, the discharge coefficient ${C_d}$ requires consideration in the nozzle control process.

3.3.2 Influence of nozzle cooling on the engine performance

According to the nozzle cooling scheme in this paper, cooling air is extracted from the engine by-pass and injected through the cooling holes on the wall of nozzle, both before and after the geometrical nozzle throat section. This cooling scheme influences the primary engine from four main aspects; each of these is discussed below.

First, the impact of air extraction from the by-pass is analogous to opening an air bleed valve there. The by-pass air flux increases and part of the core engine flux is apportioned to the by-pass. As a consequence, the whole engine flux increases and the fan operating line moves further from the surge boundary.

Second, some of the compressed by-pass air is extracted without being heated in the burner and afterburner nor expanding in the turbine. In order to maintain the LPR speed, the total temperature at the high pressure turbine inlet $T_4^*$ has to increase.

Third, part of the cooling air is injected into the nozzle before the nozzle throat and it occupies some of the nozzle flow area; as a result, the flow area for the gas is reduced. Its influence is analogous to narrowing ${A_8}$ for the nozzle without cooling, and similarly impacts the engine’s operating state.

Finally, cooling imposes a direct effect on the 2-D TV nozzle. Using the cooling air reduces the nozzle wall temperature; this benefits the nozzle life-span and improves the aircraft infrared stealthiness. In addition, the injection of cooling air at the nozzle divergent section can serve as a secondary jet and influence the nozzle flow field in the nozzle vectoring state. This impacts the nozzle thrust coefficient and the nozzle thrust vector angle.

According to the analyses above, with a properly controlled nozzle flow area, the influence of nozzle cooling on the primary engine’s operating state can be equivalent to by-pass air bleeding. Using a 0-D aeroengine overall performance simulation model, the variation of the engine’s operating point caused by cooling air extraction can be tested. According to the tests, under the flight conditions of 11km, Mach number equal to 0.8, and the afterburner being lit, increasing the cooling air mass flow extracted from the by-pass, $T_4^*$ increases approximately 0.94K per hundredth of total air flow extracted (Fig. 8), and the overall total pressure ratio decreases approximately 1.31% (1.72% for the fan) per hundredth of the total air flow extracted (Fig. 9). These results illustrate that the overuse of cooling air deteriorates the engine thermal cycle.

Figure 8.

Increase of $T_4^*$ with cooling air extraction.

Figure 9.

Decrease of fan/overall total pressure ratio with cooling air extraction.

3.3.3 Design principles for a cooled 2-D TV nozzle control schedule

The former discussion analyses the influence of using the cooled 2-D TV nozzle on the engine’s operation and overall performance. Now, some conclusions can be drawn which reveal four principles for the cooled 2-D TV nozzle control schedule design.

First, the nozzle flow area ( ${A_{8e}}$ when the nozzle is in the choked state, or ${A_9}$ in the unchoked state) is the critical factor to maintain the working conditions of the primary engine, and the nozzle discharge coefficient is needed to predict the real flow area.

Second, although the injection of cooling air benefits the nozzle structure, over extracting by-pass air causes the deterioration of the engine thermal cycle. Thus, it is better to use less nozzle cooling air once the cooling objective is achieved.

Third, as the cooling air imposes additional influence on the nozzle performance, it is necessary to introduce factors of the cooling air in nozzle performance prediction.

Finally, when extracting and using cooling air, if the nozzle throat area is properly controlled such that the cooling air injected before the nozzle throat section discharges without either reducing or expanding the gas flow area, the consequences of cooling air usage can be equivalent to that of air bleeding at the by-pass.

Here, the principles that require attention in the control of 2-D TV nozzles have been presented. In the following sections, these are adopted in the design of the nozzle control schedules.

4.1.1 Discharge coefficient

The nozzle discharge coefficient is used to represent how the non-isentropic factors and cooling air diminish the gas flow area at the nozzle throat. It is used to maintain engine working conditions by giving a proper nozzle geometry.

For cooling air is used only when the afterburner is lit, the discharge coefficient definition differs under two conditions: with and without cooling.

The discharge coefficient without cooling is defined by the following equation:

(9) \begin{equation}C_{d}=m_{g}/m_{i}\end{equation}

where, ${m_g}$ is the real mass flow of the exhaust gas, and ${m_i}$ is the ideal isentropic gas flow through the equivalent nozzle throat area ${A_{8e}}$ in the pneumatic state at the nozzle inlet. and the value of ${m_i}$ can be calculated by the following equation when the nozzle is in the choked state:

(10) \begin{equation}{m_g} = K{A_{8i}}{P_7^{*}}/{\sqrt{T_7^{\ast}} }\end{equation}

where,

(11) \begin{equation}K = \sqrt {\frac{{{\gamma _g}}}{{{R_g}}}{{\left( {\frac{2}{{{\gamma _g}+1}}} \right)}^{\frac{{{\gamma _g}+1}}{{{\gamma _g} - 1}}}}}\end{equation}

On the other hand, ${m_g}$ can be considered as the ideal isentropic gas flow through the real isentropic throat area ${A_{8i}}$ . This is presented by the following equation:

(12) \begin{equation}{m_g} = K{A_{8i}}{P_7^{*}}/{\sqrt {T_7^{\ast}} }\end{equation}

From this view, the discharge coefficient without cooling can be defined in another form as follows:

(13) \begin{equation}{C_d} = {{{A_{8i}}}/A_{8e}}\end{equation}

With this definition, ${C_d}$ can be used to produce the proper nozzle geometry.

When the afterburner is lit, the discharge coefficient with cooling can be defined by the following equation:

(14) \begin{equation}{C_{dc}} = \frac{{{m_g}}}{{K{A_{8e}}}{P_7^*}/{\sqrt {T_7^{\ast}} }}\end{equation}

In this equation, the denominator is the ideal isentropic gas flow through ${A_{8e}}$ in the pneumatic state at the nozzle inlet. It is worth noting that the form of the definition of the discharge coefficient with cooling is equal to that without cooling, so ${C_{dc}}$ can be used to give the proper geometry as ${C_d}$ . Because the cooling air injected in the front of the equivalent nozzle throat occupies part of the flow area, ${C_{dc}}$ is correspondingly smaller than ${C_d}$ on average.

4.1.2 Thrust coefficient

The nozzle thrust coefficient is used to measure the influence of the non-isentropic factors, cooling air, incomplete gas expansion, and non-axial exit gas velocity component on the jet thrust. With thrust coefficient, the nozzle thrust can be predicted.

Corresponding to the cooling air condition, the thrust coefficient differs when afterburner is lit or not.

The thrust coefficient without cooling is defined by the following equation:

(15) \begin{equation}C_{f}=F_{j}/F_{i}\end{equation}

where, ${F_j}$ is the real thrust acting on the nozzle, and $F$ is the ideal thrust when the gas isentropically fully expands. and the value of $F$ can be calculated as follows:

(16) \begin{equation}F_{i} =m_{g} \sqrt{\frac{2\gamma _{g} }{\gamma _{g} -1} \left(1-\left(\frac{P_{0} }{P_{7}^{\ast} } \right)^{\frac{\gamma _{g} -1}{\gamma _{g} } } \right)R_{g} T_{7}^{\ast} }\end{equation}

When the afterburner is lit, the thrust coefficient with cooling can be defined by the following equation:

(17) \begin{equation}C_{fc} =\frac{F_{j} }{m_{g} \sqrt{\frac{2\gamma _{g} }{\gamma _{g} -1} \left(1-\left(\frac{P_{0} }{P_{7}^{\ast} } \right)^{\frac{\gamma _{g} -1}{\gamma _{g} } } \right)R_{g} T_{7}^{\ast} } + m_{{\rm c}} \sqrt{\frac{2\gamma _{c} }{\gamma _{c} -1} (1-(\frac{P_{0} }{P_{c}^{\ast} } )^{\frac{\gamma _{c} -1}{\gamma _{c} } } )R_{c} T_{c}^{\ast} } }\end{equation}

where, the symbols with subscripts c are the parameters of the cooling air. The denominator of this equation is the thrust produced by the gas and the cooling air together on the condition that they isentropically fully expand. The cooling air mass flow ${m_{\rm{c}}}$ is subject to the same factors with the thrust coefficient under the cooling scheme where the total pressure rate of the cooling air and gas is constant. As a result, the only independent parameter of the second component in the denominator is the total temperature of the cooling air $T_c^*$ . As $T_c^*$ varies within a limited range and the thrust produced by the cooling air is relatively negligible to that of gas, this paper suggests the following simplified definition of the thrust coefficient reflects the degree of the mixed air expansion in essence:

(18) \begin{equation}C_{fc} =\frac{F_{j} }{m_{g} \sqrt{\frac{2\gamma _{g} }{\gamma _{g} -1} \left(1-\left(\frac{P_{0} }{P_{7}^{\ast} } \right)^{\frac{\gamma _{g} -1}{\gamma _{g} } } \right)R_{g} T_{7}^{\ast} } }\end{equation}

By this method, the form of the thrust coefficient definition is the same whether the afterburner is lit or not, which simplifies the prediction of nozzle thrust.

It is worth noting that because of the definition method, the thrust coefficient with cooling can exceed 1 under some circumstances, while the thrust coefficient without cooling is consistently less than 1.

4.1.3 Thrust vector angle

The nozzle thrust vector angle is used to predict the deflection of the nozzle thrust and, in turn, the axial thrust and pitching moment. As with the former performance parameters, the thrust vector angle needs to be defined for two cases: without and with cooling.

The thrust vector angle without cooling is defined as follows:

(19) \begin{equation}{\delta _f} = \arctan ({{{F_{jz}}}/{{F_{jx}}}})\end{equation}

where, ${F_{jz}}$ is the nozzle thrust in the vertical direction and ${F_{jx}}$ is the nozzle thrust in the axial direction. This paper defines ${F_{jz}}$ to be positive when the jet thrust is upward and negative otherwise. Therefore, the thrust vector angle is positive when the jet turns downwards, as with the geometrical nozzle vector angle.

The thrust vector angle with cooling can be defined in the same way:

(20) \begin{equation}{\delta _{fc}} = \arctan ({{{F_{jzc}}}/{{F_{jxc}}}})\end{equation}

4.1.4 Mass flow coefficient of cooling air

According to the cooling scheme in this paper, the cooling air is extracted from the engine by-pass and injected into the nozzle channel with a constant total pressure ratio to the gas. The mass flow coefficient of the cooling air is defined to be the corrected mass flow ratio of the cooling air to gas:

(21) \begin{equation}C_{c} ={m_{c} \sqrt{T_{c}^{\ast} } P_{g}^{\ast} \mathord{\left/ {\vphantom {m_{c} \sqrt{T_{c}^{\ast} } P_{g}^{\ast} \left(m_{g} \sqrt{T_{g}^{\ast} } P_{c}^{\ast} \right)}} \right. } \left(m_{g} \sqrt{T_{g}^{\ast} } P_{c}^{\ast} \right)}\end{equation}

As analysed in the former sections, the cooling air injected in the front of the critical section occupies some flow area, and the air injected downstream influences the gas expansion. Thus, dividing the cooling air mass flow into these two parts is necessary in a detailed nozzle flow study. The two parts of the cooling air mass flow injected into the nozzle are as follows:

(22) \begin{equation}{m_c} = {m_{c1}} + {m_{c2}}\end{equation}

where, ${m_{c1}}$ is the cooling air mass flow injected at the front of the critical section, and ${m_{c2}}$ is injected downstream of the critical section.

The mass flow coefficient of the cooling air injected at the front of the critical section is defined as follows:

(23) \begin{equation}C_{c1}=m_{c1}/m_{c}\end{equation}

At this point in the paper, the four major nozzle performance parameters have been defined. With these parameters, the discussion proceeds to the characterisation and prediction of the cooled 2-D TV nozzle performance. A set of nozzle control schedules with algorithms are put forward below.

5.2.1 Startup/idle state

When the engine operates in the startup or idle state, the major objective of the nozzle control is discharging gas. Under this condition, the nozzle control scheme is fixing the nozzle throat at the largest limit. The divergent flaps stretch straight backwards, so that the value of $\pi $ is approximately 1 and the turbines work under a high enough pressure ratio.

5.2.2 Nozzle unchoked state

When the nozzle works in the unchoked state, the nozzle flow is subsonic and the engine thrust is relatively small. Under this condition, vectored thrust is unnecessary, which means ${\delta _g}$ , ${\beta _1}$ , and ${\beta _2}$ are equal to zero degrees, so the only control parameter left is ${A_8}$ . In order to maintain the primary engine operating state, the nozzle control scheme keeps ${A_{8i}}$ equal to ${A_{8c}}$ , and the divergent flaps stretch straight backwards. The detailed nozzle control and prediction algorithm is presented in Fig. 10.

Figure 10.

Nozzle control and prediction algorithm in the unchoked state.

When the engine operating state simulation completes, the inlet parameters (i.e. ${A_{8c}}$ , $\pi $ ) are all obtained^{(Reference Sanghi, Lakshmanan and Rajasekaran64)}. Through this algorithm, a proper value for the control parameter ${A_{8c}}$ can be obtained, and the engine’s overall performance can be predicted.

5.2.3 Nozzle choked state with afterburner unlit

When the nozzle works in the choked state and the afterburner is unlit, the flow in nozzle divergent section is hypersonic and the nozzle thrust is large enough such that the vectored thrust is available. Under this condition, the nozzle control scheme adjusts the nozzle geometry with the proper control parameters to meet the control requirements. These requirements are that ${A_{8i}}$ is equal to ${A_{8c}}$ , ${\delta _g}$ is achieved, and the function between ${{{A_9}} \mathord{\left/{{A_{8i}}}\right.}}$ and $\pi $ is maintained. The detailed nozzle control and prediction algorithm is presented in Fig. 11.

Figure 11.

Nozzle control and prediction algorithm in the unchoked state with the afterburner unlit.

After these iterative processes, exact values of the nozzle control parameters (i.e. ${A_8}$ , ${\beta _1}$ , and ${\beta _2}$ ) are obtainable to guarantee the nozzle working conditions, and the nozzle thrust in the axial and vertical directions can be calculated.

5.2.3 Nozzle choked state with afterburner lit

When the afterburner is lit, the nozzle thrust boosts rapidly, and cooling air is applied at the same time. Under this circumstance, producing the nozzle control parameters is more complicated, as the engine’s overall simulation model is invoked during the calculation. The detailed nozzle control and prediction algorithm is shown in Fig. 12.

Figure 12.

Nozzle control and prediction algorithm in the choked state with the afterburner lit.

With this algorithm, the nozzle can be properly controlled with exact control parameters, ${A_8}$ , ${\beta _1}$ , and ${\beta _2}$ ; in addition, the engine performance can be predicted as well.

The nozzle control and performance prediction algorithms established in this section can be applied in the integrated modeling of the engine and the cooled 2-D TV nozzle. They are compatible with the nozzle performance definitions and characterisation. It is worth noting that the concise control algorithms presented are based on the constraints emphasised repeatedly in this paper.

Because the interpolation method of the nozzle performance is locally linear on the condition that only ${A_8}$ changes, the values of ${C_d}$ , ${C_{dc}}$ , and ${C_c}$ converge rapidly in most cases. The application of the control schedule and algorithms stated in this section are presented in the next section, where their feasibility and effectiveness are demonstrated.

6.2.1 Engine flight envelope and nozzle performance distribution

As the application case is mainly demonstrative, real engine flight envelope and nozzle experimental data are unnecessary. This paper first gives a simplified engine flight envelope. Based on the envelope, the varying ranges of $\pi $ and ${A_{8c}}$ are estimated and a synthetic nozzle performance distribution is given based on this range. With this distribution, the nozzle control and performance prediction are realised.

The demonstrative engine flight envelope used in this paper is shown in Fig. 15. This paper assumes that with this flight envelope, the region within the heavy lines are the flight conditions where the engine is able to work; only with afterburner lit can the engine fly supersonically.

Figure 15.

A demonstrative engine flight envelope.

Based on the flight envelope, the engine working points with the 0-D engine model are tested. The varying ranges of $\pi $ and ${A_{8c}}$ are obtained, and the demonstrative nozzle performance distribution can be given. The demonstrative nozzle discharge coefficient distribution with ${A_8}$ , $\pi $ , and ${\delta _g}$ when the afterburner is lit is presented in Table 1 ( ${A_8}$ is non-dimensionalised through the division by its minimum limit).

Table 1

Demonstrative nozzle discharge coefficients with the afterburner unlit

The demonstrative nozzle discharge coefficient distribution when the afterburner is lit is presented in Table 2, while other demonstrative nozzle performance parameter distributions are presented in Appendix A.

Table 2

Demonstrative nozzle discharge coefficients with the afterburner lit

Although the nozzle performance data used in this paper are synthetic and demonstrative, the generation of the nozzle performance data, such as ${C_{\rm{d}}}$ , ${{\rm{C}}_f}$ , and ${\delta _f}$ , to a great extent refers to the existing research achievements on TV nozzle performance simulation and experiments^{(Reference Wilson, Adler and Bar-Yoseph1,Reference Yang, Qitai, Wang and Zhu43,Reference Hunter44,Reference Gal-Or53)} . In addition, some essential fluid dynamic principles are considered in generating the demonstrative nozzle performance. For example, as ${A_8}$ increases, the non-isentropic effects caused by the boundary layer at the nozzle throat diminish and ${C_{\rm{d}}}$ may correspondingly increase. These principles are reflected in Tables 1 and 2.

With these given nozzle performance parameters, assuming that the divergent flaps’ area $L$ is four times as large as the nozzle throat’s minimum area, the cooled 2-D TV nozzle module can be applied on the 0-D engine model. Hence, the feasibility of the nozzle control schedule and the corresponding algorithms can be demonstrated.

6.2.2 Results of nozzle control schedule application

Based on the 0-D engine model, the integrated aeroengine/nozzle modeling method stated in this paper is realised by programming, and the demonstrative nozzle performance distributions presented in the former section are used to predict the nozzle’s working states. By testing the modified 0-D engine model, it can be demonstrated that the nozzle control and performance prediction algorithms are consistently convergent within the flight envelope. The nozzle control parameters with four significant digits can be determined in less than ten iterations of the outermost loop in each calculation.

According to the test results of the modified 0-D engine model, the engine performance and the nozzle control parameters under certain typical flight points are presented in Table 3. The values of ${A_8}$ and the engine thrust are non-dimensionalised, and ${m_c}$ is divided by ${m_g}$ .

The demonstrative nozzle performance variation with ${\delta _g}$ under the flight conditions of 15km, Mach 1.5, and in the maximum wet state is shown in Fig. 16. The test results show that over 58% thrust enhancement is gained at the cost of an approximate 20K increment of $T_4^*$ over the original model, which has an adjustable convergent nozzle. In addition, less than 5.3% of the inlet air mass flow is utilised as nozzle cooling air when the fan surge margin grows from 24.9 to over 37.2 because of the by-pass air extraction.

Table 3

Nozzle control parameters and engine performance under typical flight conditions

Figure 16.

Demonstrative nozzle performance variation with ${\delta _g}$ .

The demonstrative nozzle thrust variation with the engine’s operating state under the flight conditions of 11km, Mach 0.9, and ${\delta _g}$ equal to 0° is shown in Fig. 17.

Figure 17.

Demonstrative nozzle thrust variation with engine operating state.

The demonstrative nozzle thrust variation with Mach number under the conditions of 11km and ${\delta _g}$ equal to 0° is shown in Fig. 18.

Figure 18.

Demonstrative nozzle thrust variation with Mach number.

In order to explore the advantages on maintaining the engine operating stability of the nozzle control schedule put forward in this paper, fan surge margin variations with ${\delta _g}$ under certain flight conditions are tested. The testing results in the maximum dry state using the basic nozzle control schedule, which is simply deflecting the divergent flaps by ${\delta _g}$ , is shown in Fig. 19. Here, it can be seen that the nozzle deflections deteriorate the fan’s operating stability; however, with the recommended nozzle control schedule, due to the properly controlled nozzle throat area and the decoupled modeling architecture, the fan surge margin remains stable when the afterburner is unlit.

Figure 19.

Fan surge margin variation with ${\delta _g}$ in the maximum dry state.

The comparison of the fan surge margin variation with ${\delta _g}$ in the maximum wet state using the basic and recommended nozzle control schedules are shown in Fig. 20. When the nozzle deflection decreases the throat area, properly controlling the nozzle geometry avoids the movement of the fan operating point toward the surge boundary. Moreover, for engines that apply the recommended nozzle control schedule, because the nozzle deflection affects the cooling air mass flow (which is increasing in this paper), the fan surge margin increases slightly. Other phenomena observed in this test include that the nozzle deflection enlarges $\pi $ and reduces the engine air mass flow. These outcomes all result from the nozzle throat diminution, and can be improved by applying the nozzle control schedule put forward in this paper.

Figure 20.

Comparative fan surge margin variation with ${\delta _g}$ in the maximum wet state.

It can be seen that the modified 0-D engine model is satisfactorily able to predict the nozzle performance in the given flight envelope; in addition, the model can help to assess the benefits and costs of applying the nozzle. In future practical applications, with more detailed and precise nozzle performance data obtained from simulations and experiments, the reliability of the nozzle control parameters and performance predictions in the whole flight envelope can certainly be improved.