Danfoss Motor – Factors Affecting Motor Efficiency
 The Danfoss Motor explains: specific impulse, throat flow efficiency and thrust efficiency are three important parameters of motor efficiency, and thrust efficiency is the product of specific efficiency and throat flow efficiency, so only the specific impulse efficiency and nozzle throat are studied. Department flow efficiency. For comparison, special definitions are as follows:

  Specific impulse efficiency β, the ratio of the specific impulse calculated by the axisymmetric flow to the specific impulse calculated by the one-dimensional flow under the same conditions of the combustion chamber pressure, the nozzle expansion ratio and the expansion half angle;

  The nozzle throat flow efficiency η, the ratio of the throat flow rate calculated by the axisymmetric flow to the flow rate calculated by the one-dimensional flow.

  1. Influence of upstream radius of curvature on motor efficiency

  When the downstream radius of curvature R2/r1 = 0.625 is kept constant, the upstream radius of curvature ratio R1/r1 is calculated as: 0.3215, 0.625, 1.0, 1.25, 1.5, 2.0, 2.4, 2.75.

  When the upstream radius of curvature is relatively small, the Mach number on the wall of the throat region is much larger than the Mach number on the axis, and the Mach number on the wall of the throat region is larger, which is caused by the discontinuity of the radius of curvature of the upper and lower wall surfaces. With the gradual increase of R1/r1, the Mach number on the wall of the throat area gradually becomes smoother, and the difference between the wall and the Mach number on the axis gradually becomes smaller, and the Mach number of the throat and its downstream wall decreases.

  The upstream radius of curvature is larger than R1/r1, which has a slight increase in the specific impulse efficiency of the motor, but the effect is small. It is worth noting that in the vicinity of the upper and lower radius of curvature, the specific impulse has a significant protrusion, which is caused by the discontinuity of the flow field to the curvature of the throat wall.

  It has a significant effect on the flow efficiency of the throat, and the flow efficiency of the throat increases with the increase. The smaller the R1/r1 is, the more uneven the flow field distribution at the throat is, and the flow efficiency is reduced.

  2. Influence of downstream radius of curvature on motor efficiency

  When the upstream radius of curvature R1/r1=0.625 is kept constant, the downstream radius of curvature ratio R2/r1 is calculated as: 0.1, 0.3, 0.625, 1.0, 1.25, 1.6, 2.0, 2.4, 2.75.

  The pressure and Mach number on the wall near the nozzle and in the axial direction are smooth and continuous, except that the pressure and Mach number on the wall where the nozzle is connected downstream of the expansion cone has a turning point. The degree of turning with the R2/r1 Increasing and decreasing, this turning point is caused by the compression of the expanding airflow when it reaches the surface of the expanding cone wall. This phenomenon occurs in all nozzles. Since the airflow is compressed here, the heat transfer between the airflow and the wall surface is inevitably increased. The ablation of the thermal protection layer near here is often also severe.

  The specific impulse efficiency changes with R2/r1 as shown in Fig. 4. In the vicinity of the upper and lower radius of curvature, the specific impulse has a significant bulge. As R2/r1 increases, the Mach number distribution on the cross section of the nozzle throat region tends to be more uniform. The effect of R2/r1 on throat flow efficiency is shown in Figure 5.

  In addition, the increase of R2/r1, the Mach number of the nozzle throat and its downstream wall is reduced, so that the ablation downstream of the initial expansion zone is reduced, but for a given expansion ratio of the nozzle, the length will increase, resulting in a nozzle The increase in quality.

  3. Influence of motor efficiency on cylindrical section of nozzle

  When the radius of the arc on the nozzle and the downstream arc are equal (R1=R2=R) and the R/r1=0.625 is kept constant, the dimensionless length l/r1 of the cylindrical section of the nozzle is calculated to be 0, 0.15, 0.3. The effect on efficiency at 0.5, 1.0, 1.5, 2.0, 2.5.

  When the cylindrical section of the throat is short, the pressure on the wall is slightly twisted in the throat, but the pressure on the axis is still greater than the pressure on the wall. The Mach number distribution curve is still smooth. This means that the airflow is only slightly compressed at the throat. However, as the cylindrical section grows, the pressure and Mach number distribution on the wall appear to increase and then decrease, and the axial pressure and Mach number distribution also fluctuate slightly. With the further growth of the cylindrical section, the rapid expansion of the airflow upstream of the throat is strongly compressed by the cylindrical section, so that the pressure on the wall gradually rises and the Mach number gradually decreases. In the middle of the cylindrical section, the wall and axial pressure, the Mach number are basically It tends to be equal, and the flow clearly exhibits one-dimensional characteristics.

  It can be seen from the above analysis that the excessive length of the cylindrical section will cause the airflow in the throat to be severely compressed, thereby causing an increase in heat transfer of the airflow contrast wall. The ablation of the throat lining is enhanced.

  The effect of the length of the different cylinder segments on the flow efficiency of the nozzle throat is shown in Figure 6. It can be seen from Fig. 6 that the nozzle without the cylindrical section has the largest flow efficiency of the throat, and the nozzle with the cylindrical section. When the cylindrical section is short, the flow efficiency of the throat gradually decreases with the increase of the cylindrical section, but with the cylinder With the further growth of the segment, the flow in the throat region gradually approached the one-dimensional flow, and the efficiency of the throat flow increased, but its effect was not obvious.
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