Numerical calculation model

Numerical calculations were performed using FLUENT 6.3.26, which is a commercial fluid simulation software (ANSYS Co). Three-dimensional Reynolds-Averaged Navier-Stokes equations were used in the numerical model, and SST k-ω turbulent model was adopted to ensure that the governing equations are closed. Upwind biasing was used to determine the convection terms and central differencing to determine the viscosity terms. The temporal term was discretized using the second-order backwind form. The finite volume computational frame is based on this model. Hybrid grids were introduced in the computational zone, and the meshes near the controlling gas injection orifice were refined. The boundary condition was set according to the structure and the working character of the vortex valve variable-thrust motor: the master motor inlet adopts the mass flow inlet, the control flow injector adopts the pressure inlet, and the nozzle outlet adopts the pressure outlet. In the mass flow inlet boundary of the master motor, the mass flux is related to the propellant ignition speed, which is used during the calculation using UDF. The flow rate is determined using the formula

with ρp=1.567 g/cm³, Ap≈24.88 cm², a = 2.267, n = 0.6, m. is the master motor mass flow rate, ρp is the solid propellant density, Ap is the propellant burning area, ais the burning rate coefficient in the burning rate formula in exponential form, n is the burning rate pressure exponent, pm is pressure in the master motor combustion chamber. And in the master motor the combustion gas temperature was 1,789 K. The calculation structure sketch map and the boundary conditions are shown in Figure 2.

Figure 2:

Calculation structure schematic diagram and the boundary condition.

Calculation model checking

The results of the numerical calculation were verified with experimental results to determine the applicability and accuracy of the calculation model. The numerical calculation model was verified by comparing the pressure in the combustion chamber with those of experimental data. The experimental system is shown in [12]. The experimental system based on vortex valve includes four parts: the system supplying control flow, test motor, ignition and scheduling device and data acquisition system, as shown in Figure 3. The system supplying control flow, mainly made up of gas source, pipeline and valve, can provide necessary control flow for the experiment motor which is researched here. The ignition and scheduling device is responsible for the ignition of the rocket motor, the opening and closing of the solenoid valve and the time scheduling of the experiment. The data acquisition system is responsible for the acquisition of the pressure and the flow signal during the experiment. The chamber pressure are measured in the test. The end burning propellant which used in the tests was non-metallized propellant with n = 0.6, Tf = 1,789 K. Tf is the combustion chamber stagnation temperature. The diameter of burning area was 178 mm. The control flow used in the test was nitrogen with a temperature of 293 K. These parameters of vortex valve used in the test include the following: vortex chamber diameter of 90 mm, and control flow injector of 2-Φ2 mm (“2” represents two control flow injectors using, “Φ2” represents that the control flow injector diameter is 2 mm), and control flow injector of 1-Φ2.4 mm in the test6. The diameter of throat used in the test was 10 mm. Four tests were done with the results shown in Table 1. Table 2 shows the comparison results between experimental value and numerical value of chamber pressure. The comparison results show that the results of the numerical calculation are slightly higher than that in the experimental data with a maximum error of 9.5%. Because the thermal loss of mixed airflow, heat transfer to shell, and flow loss are not considered in the numerical calculation. Moreover, the experimental motor has a thick wall without insulation, which caused an increase in the heat loss. However, the numerical calculation result is consistent with the trend of experimental results. Thus, the numerical calculation can be completely applied in investigating vortex valve variable-thrust motors. The result also shows that the calculation result is credible within an acceptable calculation accuracy.

Figure 3:

The experimental system schematic diagram.

Performance parameter definition

Several parameters that reflect the thrust modulation performance need to be defined to ensure a better comparison of the influence of various factors. Theoretically, a higher thrust change with less control flow, lower control flow pressure, and lower pressure change in the combustion chamber can be obtained in a vortex valve variable-thrust motor with excellent performance. Therefore, parameters that reflect motor performance, such as pressure ratio and thrust ratio, mass flow rate ratio before modulation between the control flow mass flow rate and the master motor mass flow rate before modulation, mass flow rate ratio between the control flow mass flow rate and the total mass flow rate after modulation, pressure ratio between the control flow pressure and master motor combustion chamber pressure before modulation, and modulation performance efficiency, need to be defined.

Pressure ratio in the combustion chamber

Where Pm1 is the pressure in the master motor combustion chamber after modulation, Pm2 is the pressure in the master motor combustion chamber after modulation.

Thrust ratio

Where F1 is the thrust before modulation, F2 is the thrust after modulation.

Mass flow rate ratio before the control flow

Where m.c is the mass flow rate of the control flow, m.1 is the master motor mass flow rate before modulation.

Mass flow rate ratio

Where m2 is the master motor mass flow rate after modulation.

The ratio between the control flow pressure and motor combustor pressure before modulation is

Where Pcf is the pressure of the control flow.

A control flow with less flow and lower pressure must be used to ensure that the vortex valve variable-thrust motor has an excellent performance (i.e., greater thrust modulation ratio).

Influence research on vortex chamber shape

The figures in [1] and [5] show that a vortex chamber shape is not completely consistent. The kind of vortex chamber shape can ensure good motor modulation performance must be determined. Furthermore, the influence of the vortex chamber shape on modulation performance needs to be determined to optimize the vortex valve design. Thus, numerical simulations are performed to investigate the six possible shapes of a vortex chamber. These shapes are shown in Figure 4. Other construction parameters also need to be kept constant during the calculation. These parameters include the following: vortex chamber diameter of 90 mm, vortex chamber height of 5 mm, and control flow injector of 2-Φ2 mm.

Figure 4:

Vortex chamber structures.

The vortex chamber in Figure 4 is the basic vortex chamber shape. Figure 4(b)–4(e) have an additional convergent section compared with that of Figure 4(a). The convergence angle in Figure 4(b)–4(d) is 90°, and the diameters of the entrance are 20, 40, and 90 mm, respectively. The convergence angle in Figure 4(e) is 120°, and the diameter of the entrance is 90 mm. The vortex chamber in Figure 4(f) has an additional internal cone compared with that in Figure 4(d).

The control flow used in the calculation was nitrogen with a temperature of 293 K and a total pressure of 11.19 MPa. The control flow parameters at various working conditions are shown in Table 3. The calculation result of various working conditions is shown in Table 4.

Table 3 shows that the control flow significantly differs among various shapes. Moreover, the control flow increases as the space in the vortex chamber is increased.

Table 4 shows that as the diameter of the entry point is increased for four kinds of vortex chamber shapes, namely Figure 4(a)–4(d), the modulation performance appears to decrease. When the diameter of the entry point is decreased, the modulation performance increases. Comparing the results of Figure 4(d) and 4(e), increasing the convergence angle caused an increase in the modulation ratio and the impulse change rate. The calculation results of Figure 4(d) and 4(f) reveal that increasing the rear cone in the vortex chamber can improve the modulation performance, but also results in great loss. Thus, the vortex chamber in Figure 4(a) is the reasonable choice in the calculation model.

Influence research on vortex chamber diameter

In investigating the influence of the vortex chamber diameter on modulation performance, the basic parameters used are as follows: vortex chamber height of 5 mm and control flow injector of 2-Φ1.2 mm. These values are working conditions used for the vortex chamber diameters of 60, 70, 80, 100, 110, and 120 mm. The control flow used during the calculation was nitrogen with a temperature of 293 K, a total pressure of 11.19 MPa, and a control flow and mass flow rate of 0.05 kg/s. The calculated thrust modulation ratio and pressure modulation ratio are shown in Figure 5. The calculated mass flow rate ratio is shown in Figure 6.

Figure 5:

Influence of diameter on the thrust ratio and pressure ratio.

Figure 6:

Influence of diameter on the mass flow rate ratio.

Figure 5 shows that the pressure ratio and thrust ratio continuously increase as the vortex chamber diameter is increased. The pressure ratio increases faster than the thrust ratio. On the other hand, Figure 6 shows that the mass flow rate ratio continuously decreases as the vortex chamber diameter is increased. These trends conclude that increasing the vortex chamber diameter caused an increase in the momentum required to rotate the air flow into the vortex chamber using the same control flow. This phenomenon increases the modulation capability of the motor.

Influence research on vortex chamber height

The influence of vortex chamber height with varying diameters on modulation performance was also investigated. When the vortex chamber diameter is 90 mm, the control flow injector is 2-Ф2 mm. The control flow used during the calculation was nitrogen with a temperature of 293 K. When the vortex chamber diameter is 180 mm, the control flow injector is 2-Ф4 mm. The control flow used during the calculation is a gas with a temperature of 1,560 K. The control flow pressure and flow parameter used during the calculation are shown in Table 5. The calculated thrust ratio and pressure ratio using various working conditions are shown in Figure 7. The calculated mass flow rate ratio is shown in Figure 8.

Figure 7 shows that the thrust ratio and pressure ratio with two different diameters follow the same trend: the modulation ratio first increases, then decreases as the height is increased before reaching the maximum. The two maximum values of vortex valves are 7 mm for 90 mm and 9 mm for 180 mm. The diameter of the vortex chamber outlet is 14 mm when the vortex valve diameter is 90 mm, whereas the outlet diameter is 18 mm when the vortex valve diameter is 180 mm. Thus when the vortex chamber height and the outlet radius are half of the vortex chamber outlet diameter, the thrust ratio and pressure ratio of vortex valve reach maximum values. Figure 7 also shows that the modulation ratio for a vortex chamber diameter of 180 mm is much higher than that when the diameter of the vortex chamber is 90 mm. In addition, Table 5 shows that the control flow for two kinds of vortex valves is similar with a maximum error of 18%. The control flow pressure ratio of the vortex chamber with a diameter of 180 mm is higher by 5 MPa compared with that of a vortex valve with a diameter of 90 mm.

Figure 7:

Influence of height on the thrust ratio and pressure ratio.

Figure 8 shows that the master motor gas mass flow rate of the control flow of the vortex chamber with a diameter of 90 mm increases after modulation. Figures 7 and 8 show that the modulation performance of the vortex chamber with a diameter of 180 mm is significantly higher than the vortex valve with a diameter of 90 mm, which indicates that the modulation performance of a vortex chamber with a hot gas control flow is higher than that with cold airflow conditioning control flow.

Figure 8:

Influence of height on the mass flow rate ratio.