Effect of modification in flow distributor valve 2 geometry on the pressure drop and chamber 3 pressures , in numerical and analytical way , in ORBIT 4 Motor HST unit 5

In this paper, an attempt has been made to analyze the effect of spool port/ groove 14 geometry on the pressure drop and chamber pressures which effect the performance parameters of 15 the flow distributor valve. The work mainly involves formulation of detailed mathematical model 16 of the valve and compare them on the same platform. For mathematical modelling, Matlab has 17 been used. The size of the orifices is considered same throughout the model for better comparison. 18 Initially the construction and functioning of flow distributor valve along with working principles 19 of hydrostatic motor (Rotary Piston) is shown. Next shown the analytical analysis of area change 20 and pressure drops due to different geometry of the spool valve ports. After that the computational 21 fluid dynamics (CFD) analysis has been shown. A complete mathematical model to describe such 22 flow distributor valve is developed after having a comprehensive knowledge of orifice 23 characteristics, flow interactions based on valve geometry. Equations of flow through different 24 orifices (fixed and variable area) of the valve have been developed based on the relationships 25 obtained earlier. 26


Introduction
Rotary Piston Machines (Orbit motors/ Gerotors) are in the category of positive displacement machines which are similar to the rotor dynamic machines in construction because of the presence of rotating member (star/ rotor) and its envelope (ring/ stator).There are two basic types of rotary piston hydrostatic units.One is the fixed axis (Gerotor) unit in which kidney port type valve is used.
The other one is floating axis type orbital rotor (Orbit) unit in which the pintle type or commutator type port valve is used.Although these valves are widely used in various types of hydrostatic units, but no theoretical guidelines are available in the open literature regarding their design specifications (i.e.their port sequence, geometry, positions etc.) particularly for ROPIMAs operations.In orbit motor, pressurized fluid is forced into a chamber, it causes the inner member rotate about its own axis and revolve around the stator centre.As the angular position of the inner member changes with respect to a chamber as it is being filled with fluid, at a certain angle (depending upon the design parameters) the adjacent chamber begins to fill with pressurized fluid.Once a chamber reaches its maximum volume, the fluid inside this chamber is forcing the rotor to change the chamber position.
The pressure on the inner member and by entering the pressurized fluid to the adjacent chamber causes the continue rotation of the rotor.R Maiti [1] carried out an extensive experimental analysis to improve the performances of LSHT hydraulic motor by lead and lag of the distributor valve timing.It was noticed that torque efficiency was different due to the torsional deflection of the shaft in which the valve is embedded.
Gamez-Montero and Codina [2] has evaluated the flow characteristic of a trochoidal-gear pump analytically and experimentally to understand the performance of a trochoidal-gear pump.Again Gamez-Montero and Codina [3] estimated the leakage, instantaneous flow, the flow ripple experimentally.Marko Simic, Mihael Debevec and Niko Herakovic [4] have designed valve with different metering edges of the spool and to quickly check through simulation how the valve influences the characteristics of a practical hydraulic system using analytical or CFD simulation packages.
In the present work pintle type spool valve, which is one type of flow distributor valve, is used to supply the fluid to the expansion and compression chambers of the hydrostatic motor/ pump.The inlet-outlet port sequence of the flow distributor valve is determined from the duration of phases The pintle valve used in hydrostatic units has a unique design [5].The valve is integral with the output (same as rotary motion of inner member/ star) shaft.Opposite to the output end, the shaft is hollow and houses inner side of one end of gear coupling type cardon shaft.The other end of the cardon shaft is coupled to the inner member i.e. 'star'.Thus the rotation of the inner member about its own axis is transmitted to the output shaft.
On the valve body there are two circumferential grooves which are aligned to two port holes for inlet and outlet flows, in the housing.Between these two grooves there are eqispaced grooves, equal to the twice the number of lobes of star member(in present analysis twelve in numbers), in transverse direction.Each alternate transverse grooves connect to a common circumferential groove of the valve and this common circumferential groove again aligned to portholes (seven in numbers) in housing connected to the chambers.The uniqueness in the valve design is such that the set of transverse grooves connecting the inlet will be connected to the chambers in expansion mode and the other set connecting to the outlet will connect the chambers in compression mode.The intermediate grooves will remain disconnected.These sequences can be realized from Figure 1.
The housing of the OMR 80 (Danfoss) motor has seven pathways (cylindrical).These pathways can be seen in Figure 2, which shows the top and sectional view of housing and also shows the

Geometric Modeling of Flow Distributor Valve
The main focus is the geometric modeling of flow distributor valve (shown in Figure 4) and the valve opening area for different angular position of the main shaft.Solid Works software is used for this geometric modeling.The rotary motion of hydrostatic motor (OMR 80) results a direct and rotary spool movement of the flow distributor valve which in turn modulates the flow of fluid through the port of the valve.The orifices of the flow distributor valve are formed by the matching between the square wave shaped convex lands on the spool and rectangular (kidney type) holes on the sleeve (i.e.motor housing).

For 2 Degree of Index Angle geometric modeling
The effective orifice areas are determined by the rotational speed (ω ) of the spool.If the spool rotation angle from neutral position is denoted by θ and index angle as ϕ then the orifice area can be calculated as : In Figure 5   (i) Opening of a single spool valve port is considered at a time.
(ii) The hydrostatic motor chamber is at the beginning of an expansion phases in which fluid is supplied at a specific pressure from the port.pressure drop takes place.As the further displacement of the shaft takes place the graph (shown in Figure 7) becomes linear, and then again parabolic at the maximum opening of kidney port [4,6].

Mathematical modeling
The basic equation developed to represent steady-state fluid flow is the Bernoulli equation which assumes that total mechanical energy is conserved for steady, incompressible, inviscid, isothermal flow.Bernoulli's equation for pressure drop at the orifice is given as: So pressure drop is given as: is shown in Figure 9 below for all 7 kidney ports of the hydrostatic unit.It is observed from the plot that rate of change of area opening for all spool ports/grooves is symmetric and has a constant phase difference.

For 1 Degree of Index Angle of Spool Valve/Port
A small local pressure drop is preferred to minimize the ripple effect and cavitations risk.The optimization of an orifice geometry involves the investigation the effect of its geometry on the pressure drop, flow rate and flow ripples.Any unfavorable behavior may degrade the performance of the hydrostatic motor/pump.Figure 10 shows the interaction of spool valve port with the kidney port of the hydrostatic motor for 1 degree of spool valve index angle.Figure 11 shows the interaction of spool valve port with the kidney port of the hydrostatic motor for 3 degree of spool valve index angle.

For 0 Degree of Index Angle of Spool Valve/Port
Figure 12 shows the interaction of spool valve port with the kidney port of the hydrostatic motor for 3 degree of spool valve index angle.(ii) By using different geometry (change in the index angle of the groove) of the spool valve, it can be shown that the improvement in pressure drop characteristics of the flow distributor valve (pintle type) is possible.For a fixed flow rate, the pressure drop is regulated more smoothly by increasing the index angle of the spool groove from zero degree to 3 degrees.In this analysis four  (iii) As the objective is to attain optimum valve geometry without compromising the performance of the hydrostatic motor.It is observed from the analysis that for different geometries of the spool groove at constant flow rate (5 lpm), means spool groove with higher index angle gives much more smooth and regularized pressure drop curve, which in turn smoothens the pressure ripples applied into the chambers of the hydrostatic motor chambers, shown in Figure 15.Thus more continuous and gradual pressure applied reduces the pressure ripples and thus erratic operation of the motor is avoided.In this way these hydrostatic units can be used for more precision and highly sophisticated operations.

CFD (Fluent) Analysis
To analyze the fluid flow through the "flow passage of stator housing", ANSYS/Fluent software is used.To do the CFD analysis, firstly develop the 3-D model of the flow channel for different angular opening of kidney port using solid works software.After developing different flow channel models, simulation has been done using CFD technique in Fluent® environment.

Analysis of Fluid Flow through "Flow Passage of Stator Housing"
By importing the solid model of fluid flow channel in fluent module of ANSYS software, a 3-D meshed model (Figure 16) with variable fineness is developed using these parameters stated in table 2 below.For this SOLID186 element has been chosen, which is a higher order 3-D 20-nodes (each node has three degree of freedom) solid element that exhibits quadratic displacement behavior.It

Results and Discussions
After analyzing the pressure and the velocity vector for different index angle of the spool valve the common observation are as under:  For the opening of 0.316 mm of spool groove linear displacement i.e. which is equal to 0.857 degree of spool valve shaft rotation from initial neutral position, the pressure on other side of orifice opening is very high because the major pressure drop takes place at less than 0.25 mm of opening.


As the opening is increased gradually, the pressure increase is continuous and follow the analytical results.Thus the FLUENT results are comparable with the analytical results.


Velocity vector also follow the continuous pattern, for less opening of spool groove the velocities are very high at the orifice and gradually reduce, on increase in the opening.


The pressure and velocity profile is continuous and regular and no irregularities are observed through the fluid flow path.
(e) Static pressure for 2 0 index angle 0.316 mm port opening.
(f) Velocity vector for 2 0 index angle 0.316 mm port opening.
(h) Velocity vector for 3 0 index angle 0.316 mm port opening.
(g) Static pressure for 3 0 index angle 0.316 mm port opening.
(i.e.expansion and compression) of chambers in terms of input/ output shaft rotation for a single cylinder as well as multi-cylinder units.Very few amount of work has been done on the geometric features of the flow distributor valve and regarding that the information's are also rare in open literature.Various performance parameters like flow, pressure, speed, and torque affect the overall efficiency of rotary piston machine.Out of these, this study is focused on the characteristics of the flow phenomenon in "flow distributor valve (pintle type rotary spool valve)" within the ambit of theoretical study and numerical analysis.The behavior of fluid flow through valve passages has been studied with accuracy considering actual operating conditions with the help of CFD simulation technique.The main objective of the present investigation is to analyze the effect of different spool groove geometries on the pressure drop, chamber pressures and pressure distribution along the fluid flow passage of an epitrochoid generated rotor stator hydrostatic unit (Orbit Motor).

Figure 1 .
Figure 1.Flow distributor valve of an orbit motor.

Figure 2 .Table 1 .
Figure 2.The technical specifications of flow distributor valve of the orbit motor (OMR-80) is shown in table 1.The sequence of flow in flow distributor valve is shown in Figure 3.

Figure 3 .
Figure 3. Sequence of flow in flow distributor valve.

Figure 2 .
Figure 2. Highlighting pathways to chamber top and sectional view of OMR 80 (danfoss) hydrostatic motor.
shows the initial displacement of opening (where x = radius of shaft (r) x angle of rotation () x180/) and as the shaft rotation takes place, the spool valve start opening of its axial slots into Output shaft end Outlet annular common pool Outlet spool port

Figure 7 .
Figure 7. Valve opening area vs output shaft rotation.

Figure 13 .
Figure 13.Spool valve opening due to shaft rotation vs opening area change.

Figure 14 .
Figure 14.At 5 lpm flow rate, chamber pressure due to spool valve opening and change in valve index angle (in Deg.) also has mixed formulation capability for simulating fluid flow of incompressible fluids.In this analysis computational fluid dynamics (CFD) FLUENT is used to investigate the effect of groove geometry and its sizes on the flow properties for a single groove at the flow distributor valve of the hydrostatic unit.After analyzing, the streamline velocities and pressure distributions in the groove region and the flow path up to the chambers for various geometric designs of the spool groove are obtained.For square shaped spool groove the streamline velocities and leakages are highly affected.Streamlines can give a qualitative idea about the flow of fluid through the fluid passage, if any irregularities of flow exist, in that case, where they develop and what influences they have on the hydrodynamic performance of the flow distributor valve.

Figure 15 .Figure 17
Figure 15.At 5 lpm flow rate, pressure drop due to spool valve opening and change in valve index angle (in Deg.)

Figure 16 .
Figure 16.Meshed model for all different index angle at 0.316 mm opening.