Estimation of the mass of the centrifugal electric pump unit of the spacecraft thermal control system

. The article deals with the problem of estimating the mass of a centrifugal electric pump unit of a spacecraft thermal control system at the stage of preliminary design. The energy parameters of the electric pump are considered as the initial information relevant for the specified assessment: mass and volume flow (m 3 /sec), head H (Joule/kg) and speed factor n s (dimensionless parameter). Based on the known data, using a third-order equation, an approximation of the graphical dependence of the reduced mass of aggregates on the mass flow rate of the coolant (kg/sec) was carried out. An analysis of the equation showed that starting from the value =0.15 kg/sec, the dependence becomes asymptotic, indicating the invariance of the reduced mass of the unit with a further increase in flow. The obtained dependence, covering a narrow range of variation, does not allow us to evaluate the changes of the reduced mass of the unit when designing a unified series of designs of the centrifugal electric pump unit of the spacecraft thermal control system, taking into account changes in such energy parameters as head, volume flow and speed coefficient. Therefore, at the 2nd stage of the study, an analysis of the influence of these parameters was carried out within the framework of the graph = f ( Н ), containing the level lines n s = const and = const. It follows from the graph that if the increase in pressure H is due to an increase in the number of revolutions of the rotor, then such a modification of the unit is not accompanied by an increase in the radial dimensions and absolute mass of the design of the centrifugal electric pump unit.

the reduced mass of aggregates on the mass flow rate of the coolant (kg/sec) was carried out.An analysis of the equation showed that starting from the value =0.15 kg/sec, the dependence becomes asymptotic, indicating the invariance of the reduced mass of the unit with a further increase in flow.The obtained dependence, covering a narrow range of variation, does not allow us to evaluate the changes of the reduced mass of the unit when designing a unified series of designs of the centrifugal electric pump unit of the spacecraft thermal control system, taking into account changes in such energy parameters as head, volume flow and speed coefficient.Therefore, at the 2nd stage of the study, an analysis of the influence of these parameters was carried out within the framework of the graph = f (Н), containing the level lines ns = const and = const.It follows from the graph that if the increase in pressure H is due to an increase in the number of revolutions of the rotor, then such a modification of the unit is not accompanied by an increase in the radial dimensions and absolute mass of the design of the centrifugal electric pump unit.
The degree of perfection of spacecraft systems is estimated by the specific power equal to the ratio of the system's power to its mass.For example, the specific power of the thermal control system of modern spacecraft lies in the range of 30-37 W/kg at a thermal power of 10 kW and a service life of 15 years [8][9][10][11].The task was set to bring the degree of perfection of the TCS to values of 45...50 W/kg, with a service life of 25 -35 years and a power of more than 20...30 kW.

Description of the design of the centrifugal electric pump unit
On Fig. 1 shows a cross-section of the unit, consisting of an impeller 1 and a DC electric motor, including an armature 2 and a sealed stator 3. When fixing the impeller 1 on the shaft of such an engine, it is not necessary to install an end seal and seal the cavities of the impeller and electric motor between themselves.Therefore, the cavity between the armature 2 and the stator 3 is filled with coolant (in Fig. 1 it is shaded in gray).The armature of the engine 2 is made in the form of a permanent magnet.Engine stator 3 is an outer housing with a package of active iron pressed into it.Screen 4 installed between armature 2 and stator 3 is made of non-magnetic stainless steel in the form of a cylinder hermetically connected to the motor casing.Screen 4 fits snugly against the inner surface of stator 3.Because of screen 4, the efficiency of the electric motor is lower due to additional losses in the screen and in the gap between armature 2 and stator 3. The gap can reach a value of the order of 0.8 10 -3 m, including screen thickness.
One of the directions for solving the problem is to increase the reduced mass of the centrifugal electric pump unit , where M is the mass of the CEPU (kg), m is the mass flow rate of the coolant (kg/sec).In the pressure characteristics of CEPU, not mass, but volume flow V (m 3 /s) is often used, the relationship between which is characterized by the formula

/ m V
, where is the density of the coolant (kg/m 3 ).The position sensor is located in the same housing with the electric motor, including the position sensor rotor 5 and the position sensor stator 6.The position sensor rotor 5 has the form of a segment (beveled cylinder) located on the same shaft with the engine.The segment performs the function of the signal element of the position sensor.Sensing elements are located on the stator of the position sensor.Their number is equal to the number of motor windings, and the position corresponds to the position of the corresponding windings.Hall sensors, magnetic diodes, etc. can be used as sensitive elements.Under the influence of the signal element, they generate control signals entering the switch.The commutator is assembled from semiconductor elements and mounted in a separate box connected to the electric motor with a pin connector.

Hydraulic parameters of the centrifugal electric pump unit
The flow rate of the liquid coolant V in the circulation circuit of the spacecraft thermal control systems, which provides the specified heat removal mode, is estimated by the dependence: where т Q -thermal load (W); c is the heat capacity of the coolant (Joule (kg K)); t - heating of the coolant in the cooling path TCS (K).
The pressure loss phr due to the hydraulic resistance of the circulation path of the TCS spacecraft is due to two components: The typical phr level of the circulation paths of the TCS spacecraft lies in the range of phr= (0.01...0.1)MPa [12][13][14].

Materials and methods
Low-flow centrifugal electric pump units TCS spacecraft with angular speed = n/30 (sec - 1 ) in the range of values = (400…1000) sec -1 and volumetric flow rate V 300 10 -3 m 3 /sec belong to the class low-speed blade machines [5,12].At the required pressure H, equivalent to phr at the heat carrier density =800 kg/m 3 , that is Н=(12.5…125)Joule/kg the speed factor of the aggregates ns lies in the range ns=40…60 [15].

) m ( f M m
The reduced mass of a centrifugal pump m M depends on: The first 2 parameters of a centrifugal pump characterize the efficiency of energy conversion in it.The number of revolutions n affects the intensity of energy transfer.When designing CEPU TCS spacecraft, developers to ensure the highest values of the specified parameters.
In the work [16], on the basis of empirical data, the graph

Results
The universal parameter that characterizes the influence of the energy parameters H, V and on the geometry of the CEPU impeller is the coefficient of speed ns: On Fig.For all 3 schemes of changing the pressure H, the volumetric flow rate of the working fluid and the speed coefficient ns, the boundaries of the trajectories AB, AC, AD are on the lines of the level with a lower value m M .In particular, on the graph, points B, C and D are located on the same level line m M = 15 sec, whereas point A is located on the line m M = 20 sec.This means that the use of design solutions traditionally used in the design of the CEPU TCS spacecraft, the development of a high-power unit should be accompanied by an improvement in the specific mass characteristics of the construction.

Discussion
A separate comment requires an analysis of the result of the application of option 1.An increase in the pressure H due to a decrease in the speed coefficient ns = const and n = const is accompanied by an increase in the radial dimensions and absolute mass of the centrifugal electric pump design.Obviously, within the given parameter m M , this should be accompanied by an increase in the value of M, which contradicts scheme 1.On the other hand, if the growth of H is due to an increase in n, with a narrowing of the meridional section of the impeller channels, or an increase in the pressure coefficient, then such a modification of the CEPU meets the conditions for the implementation of scheme 1.This contradiction is due to the fact that the graphical dependence in Fig. 1  An increase in the pressure coefficient H, rather than the number of rotations of the rotor n, is more preferable, since it is not accompanied by a deterioration in the anti-cavitation qualities of the CEPU and a decrease in the service life of the bearing units of the unit.However, such an approach requires time-consuming studies of the hydrodynamics of the flow in the cavity of the vessel and the improvement of for designing its flow form.
In general, the analysis carried out is of an evaluative nature in the preliminary design and planning of CEPU TCS spacecraft measures aimed at improving the specific mass indicators of centrifugal electric pump units

Fig. 2 .Fig. 2 .
Fig. 2. Approximation of this graphical dependence in the form of equation 3 is described by formula (3):

3 ,m
in the axes the coordinate OH V , for the conditions: n= 6000 rpm, = 800 kg/m 3 , the level lines ns= const and m M = const, in order to illustrate the possible analysis of various schemes, changing the power of the unit using the parameters H, and ns when transition from point A (Hinitial, V initial) according to the following 3 options: • The AB line characterizes the variant H=var, V = const, ns = var, , kg/sec E3S Web of Conferences 431, 02001 (2023) ITSE-2023 https://doi.org/10.1051/e3sconf/202343102001• The AC line characterizes the variant H = var, V =var, ns= const, • The AB line characterizes the variant V =var, H = const, ns= var.