Resistance moment of a rotation surface of liquid rocket engines turbomachines elements

The research elaborates the main characteristics of the liquid propellant engines; it determines that some turbo pump units have got the frequency of rotor spinning up to 100 000 and even 120 000 r.p.m. The authors analyse the current methodologies to specify losses connected with disc friction. The methodologies determining disc friction coefficient often obtain criterion-empirical character, and due to increasing a number of rotor spinning of turbo pump unit of the liquid propellant engines, they reflect the specification reliability inaccurately. The research demonstrates equations to determine disk friction coefficients based on considering the theory of three-dimensional boundary layer to a rotational flow taking into account the turbulent process of velocity distribution. The authors give recommendations on determining an index of velocity distribution degree depending on Reynolds rotation criterion of a disc and plug flow.


Introduction
The major part of the existing methodologies to calculate flow parts of turbo pump units (TPU) of the liquid propellant engines (LPE) is of criterion-empirical character; it is used for the nod boundary conditions and feeding units of the liquid propellant engines obtaining rotation frequency approximately 20 000 -40 000 rotations per minute. The current TPU of the liquid propellant engines obtain comparatively high rotation frequency and it can be up to 120 000 rotations per minute. The fact does not consider the degree of the turbulent process of flow velocity distribution in the three-dimensional boundary layer of the elements of the flow range of the feeding units and it requires additional research and specifications of the used dependencies due to changing boundary conditions.
While designing current rocket engines and converting to environmental fuel components, there is a tendency to increase rotation frequency of TPU. That results in increasing in pressure produced by a pumping stage, growing a pump speed coefficient as upgrading the efficiency of the pump and the turbine, decreasing the dimensions such as reducing the axial and radial loads to the rotor and as a consequence it leads to TPU mass reduction in general.
Multiple discrepant values are provided by the numerous experimental and theoretical research conducted by scientists within a range of geometrical and performance parameters of flows in the rotorstator gap [1][2][3][4][5][6][7][8][9]. Some methodologies to calculate resistant torque obtains various disadvantages first of all connected with applying empirical coefficients; they do not consider the availability of the radial component of the absolute velocity in the side cave. One of the main tendencies to develop aerospace engineering is to improve the design quality based on using the current calculation methodologies and mathematical models reflecting the processes in both separate units and in the whole airborne vehicle in general.
While designing, the requirements to TPU configure due to the assignments performed by the power unit (PU), where TPU is an element constituent and with which it assembles as a single block. The requirements to the PU belong to TPU as well: to provide feeding fuel components with the flow requirement and pressure under high degree of reliability and efficiency in all operational modes of the engine; to provide minimal dimensions and mass; the construction simplicity and minimal cost.

Specifying disk friction coefficient
The power balance of a centrifugal-type pump are consider where the power output of the centrifugaltype pump is calculated as Calculates a disk friction coefficient taking into account increasing rotation frequency of TPU of LPE. While realizing turbulent flow, originally, the power law of airfoil shape distribution of speed in the boundary layer [10] is applied where M, L, H, J, K -relative characteristic quantities of the dynamic three-dimensional boundary layer [10]. The momentum losses thickness rotationally with a certain airfoil shape for a disc is where  = d -f, d -disk angular velocity, f -flow angular velocity, and Reynolds criteria for disk Enter a variable to replace: Assuming the expressions for the momentum thickness rotationally, the friction induced shear stress on the wall is determined as and on the disc it is The equation for disc friction loss coefficient for a rotor wheel is Therefore, the friction coefficient equation for a rotational wall is and for the friction coefficient for a disc rotationally, the equation is Should to take into account that when the disc losses is depend on the disc and wall frictions [5], therefore, the disc friction loss coefficient is determined as Also should to take into account the following: to determine disc friction loss coefficient and, thus, disc losses should be aware of distributing angular velocity of the plug flow f  depending on disc angular velocity d  , that requires to solve a differential equation [10] ( ) where leak V -seal leakage. A sophisticated assignment is to specify analytical dependence of angular velocity of the plug flow   A separate assignment is to determine an airfoil shape m depending on the criterion Re of the plug flow and Re of the disc. When the disc friction and thermal efficiency in the rotary cavities are specified depending on the mode parameters (Reynolds criterion) of the earlier obtained airfoil shape degree of the function of distributing flow velocity, recommended to consider m=911 at the disc and m=79 at a wall. Reynolds criterion at the disc is determined with angular velocity of a pump wheel disc (4) or a turbine.

Conclusion
The obtained equations for the disc friction loss coefficients allow to determine the efficiency loss to the disc friction in the TPU of LPE centrifugal-type pumps. Comparing with the empirical dependencies obtained by other researchers, using degree m of the turbulent dynamic three-dimensional boundary layer significantly increase the range of the area and reliable determination of the disc friction.