International Journal of Fluid Machinery and Systems DOI: http://dx.doi.org/10.5293/IJFMS.2019.13.1.136 Vol. 13, No. 1, January-March 2020 ISSN (Online): 1882-9554

Original Paper

Modeling of the Manifold Configuration for Maximum Efficiency in a Hydraulic Machine

Kesar M Kothari 1, R.Udayakumar1, Ram Karthikeyan1, Vishweshwar S1and Nikitha Raj2

1Department of Mechanical Engineering, Bits Pilani Dubai Campus Dubai, United Arab Emirates, [email protected], [email protected], [email protected], [email protected] 2Department of Electrical & Electronics Engineering, Bits Pilani Dubai Campus Dubai, United Arab Emirates, [email protected]

Abstract

Hydraulic manifolds are metal cuboids machined to realize the compact circuit layout within them. They are introduced in the hydraulic machines to fit the large and complex hydraulic system layouts in narrow spaces available in the machines. Therefore, designing of the manifold in fact is more oriented towards achieving minimum size and weight. But the use of manifold, may introduce high pressure losses in the system. Efficiency of the system decreases and temperature of the fluid increases with pressure drop. This present research work focuses on understanding the pressure losses in the most common channel connections used in the manifold to realize the hydraulic circuit and to understand the efficiency of the manifold at different flow values. To achieve these objectives, a real-time case study is considered, where a manifold for a cable pulling winch machine is modified to reduce the pressure drop and increase the efficiency of the machine. Simple channel models are considered and analyzed using semi empirical equations available in the literature and are compared with results obtained from Computational Fluid Dynamics (CFD) analysis. Various geometric bend models are drafted in Solid Works and then exported to do the CFD software to obtain the pressure drop with different flows. The values obtained from CFD and the characteristic of the valves from the manufacturer’s catalogue are used to create the manifold in Matlab Simulink to predict the performance of the manifold at different flows. Therefore, with these results, the overall hydraulic efficiency of the winch is determined.

Keywords: CFD analysis; Efficiency; ; Manifolds; Matlab Simulink; Pressure Drop; Solid Works

1. Introduction The science involving the generation of power by utilizing the mechanical properties of fluids encloses the principles of hydraulics. The applications of hydraulics are used to generate, control and transmit power using pressurized liquids. or modern mobile hydraulic equipment use a typical hydraulic circuit in which the pressurized fluid is transferred from hydraulic pumps to different (hydraulic motors and cylinders) through pipes, conduits, channels and valves. The extensive use of this mechanism in drive trains is mainly due to excellent power to weight ratio of the and large forces produced over a moderate distance. The purpose of the system may be to control the fluid flow or to control the fluid pressure. Hydraulic circuits, in mobile applications such as off-road applications, must fit in the narrow spaces available in the machines and guarantee functionality with acceptable efficiency. So, the hydraulic manifolds are used, which contains compact circuit layouts and can be fitted in a small space. A hydraulic manifold is a rectangular metal block machined to achieve minimum size, less weight and simplify the complex hydraulic circuit layout by logically interlinking the different elements of the internal mechanism of the winch hydraulics. The blocks are drilled through to create internal channels and oil circulation passages which are fitted with screwed cartridge valves. A general drawback for developing a manifold is its high-pressure loss and unwanted temperature rise when manufactured compactly. The efficiency of the hydraulic machine is reduced due to unwanted losses in a compact manifold as well as due to the losses experienced by the other components. So, the designing of the manifold with less pressure drop and good heat dissipation is extremely important. In the past, researches on the manifolds were mainly focused on minimum block size or less volume and mechanical strength.

Received November 25 2018; revised January 19 2019; accepted for publication August 02 2019: Review conducted by Xuelin Tang. (Paper number O18052C) Corresponding author: R.Udayakumar, [email protected]

136 2. Literature Review Efficiency of a hydraulic system is the major concern in the industry. In the past, attempts were made to design the manifold blocks in an automated way [1]. The design was focused on fabricating the smallest block possible using the complex machining. Designing hydraulic manifold blocks consisted of placing components and tapping holes on the block and placing oil circulation drillings according to the hydraulic schematic. The optimum result, i.e. a minimum block size, often implies to a rather complicated set of drillings to bring oil circulation between external ports of the components [2]. Nowadays fuel cost, fuel availability and the elimination of pollutants due to the burning of fuel are considered as a priority. So, designs are more focused on the efficiency of the system by reducing the losses in the system. Designing the manifold must focus on the decrease in pressure loss, evaluating heat generation and heat transfer in the system and also analyzing the flow through the passages. Wang J performed a consistent review of different methods to study the flow in manifolds where CFD with discrete and analytical models are analyzed. He even stated that a CFD model is suitable for optimizing the geometry of a manifold that may be too expensive from the point of view of time and computational effort [3]. Yang and Liu et al. studied the effects of different guide vane structures on tangential velocity distribution due to the Rankine vortex characteristics, and the corresponding impacts on the pressure drop[4]. Zhang and Zhou et al. researched numerically the influences of blade profile on velocity distribution, pressure distribution, and flow regulation pattern in the vicinity of an impeller of a centrifugal pump[5]. Heng Wang et al. presented two optimized designs of a commonly-used fluid distribution manifold having one entrance and six exits. Numerical simulations were carried out to optimize the dimensions and mechanisms of these proposed designs for the sake of enhancing the uniformity of fluid distribution amongst the exits and reducing the formation of dead zones inside the manifold cavities [6]. Missirlis D and Jones G.F on the other hand, studied the design parameters that can strongly affect the flow distribution and consequent heat transfer [7-8]. The main losses in the hydraulic systems come from pumps, motors and valves controlling the actuators. According to Lanke’s article the estimation of the impact of the U.S Fluid power industry resulted that the average efficiency of the hydraulic systems in the industrial applications is 50% and drops to 21% for mobile applications [9]. Even a little improvement in efficiency may have greater impact on fuel consumption. So, every component and every aspect of the hydraulic system should be considered carefully. Martinopoulos et al illustrated some examples for the application of CFD on manifolds which are helpful to analyze the flow inside solar collectors that are characterized by complex geometries thus allowing to identify critical regions that can compromise the efficiency [10]. Murrenhoff et al [11] describes the most recent energy-efficient hydraulic architectures for mobile applications. Changing the valve systems in which independent metering or digital valves can be used instead of the traditional ones. Moreover, pump- controlled systems which eliminate the directional valves and energy recovery systems which uses energy from braking or lowering of loads can recover hydraulic energy with accumulators and hydraulic motors. Empirical equations available in the literature are derived for simple bends and connections. These equations cannot be used for evaluating complex connections inside manifold. Internal channels may be present with multiple bends with different curvature values and different diameter sizes. For a singular particular case experiment, measurement of CFD analysis is the only resource to have correct estimation. Moreover, 2D and 3D CFD analysis have proven to be affordable when applied to study the flow through pipes as shown for example in [12]. Abe et al. in two research publications (Pressure drop of pipe flow in manifold block and Flow analysis in pipe of a manifold block respectively) used CFD analysis to analyze pressure drop through a complicated internal passage with multiple elbows for which empirical formulation could not be applied. Thus, it was proved that CFD was assessed to be an effective method to evaluate pressure drop even if a certain gap between the numerical and experimental results were evident [13-14]. Zhong L et al. performed an analysis on a rectangular asymmetric three-dimensional diffuser to assess the performance of a standard k-ε turbulence model for separated flows [15]. Song Z.A in the research and analysis of the resistance characteristic of combined flow channel confirmed the results obtained by applying CFD analysis to a hydraulic manifold with the bend geometries [16]. Idelchik I.E in his Handbook of Hydraulic Resistance and Murakami M in his study of fluid flow in three-dimensional bend conduits, together illustrated an example for the single elbow in which change of direction of flow in curved channels caused the formation of centrifugal forces directed from the center of curvature toward the outer wall [17 -18]. While many studies have been done in the past on single 90°-degree bend passages, finding the “loss coefficient” for the elevation of pressure drop can be difficult due to generalized rules for the design [19]. While studying the pump efficiency’s uncertainty considerations [20], Manring N.D considered a case with two independent pressure sensors to sum up the accuracy to measure the pressure drop. From this, the percentage uncertainty can be easily determined. Merritt estimated the entry length for different types of flow depending on the Reynolds number for laminar flow and approximated with different formulas for turbulent flow in which influence of Reynolds number is weaker [21]. Therefore, efficiency of the system can be increased by reducing the pressure losses in the fluid flowing in the hydraulic circuit. Pressure losses in the system increase the pressure levels in the system to a high value to perform the required task. Also, pressure drop causes the additional generation of heat in the system that must be removed.

3. Gap in Existing Literature The existing literature only contains specific results regarding hydraulic losses obtained from CFD analysis by considering various individual bends in the manifold and the experimental data had been compared to it. Many computational models had been discussed and compared to obtain the most precise method to perform the computational analysis. In the present research, we have considered values of the CFD analysis for the losses in the manifold bends but by incorporating them with a software called MATLAB, we designed a holistic manifold model to understand the efficiency and performance of the complete machine. Therefore, in this research, the objective is to focus on the pressure losses in multiple commonly used channel connections drilled into the manifold, thus, comprehending the efficiency of the manifold. The multiple channels can be complex and vary in curvature, circumference and diameters. For this purpose, a manifold for the cable pulling winch machine is used to study the internal pressure losses and the efficiency of the machine is calculated at various flow rates. This study is computed using Computational Fluid Dynamics

137 (CFD) and with mathematical modeling to foresee the results of pressure drops. Simulations are validated using semi- empirical equations to calculate the accuracy of the results of the fluid flow through the manifold. These results will be combined to calculate the efficiency of the overall winch machine.

4. Explanation of Hydraulic Circuit In the cable pulling winch machine the hydraulic circuit assists in powering the motors by regulating the pressure and flow to the system by using valves such as pressure relief valve, sequence valve, directional control valve and check valve. A typical hydraulic circuit for the cable pulling winch machine with a minimum number of valves is given in Fig. 1. and a manifold is manufactured using the circuit as reference. A 3D CAD (computer-aided design) model of the manifold is given in Fig. 2. In the Fig. 1. the letters B, B1, B2 , B3 are input ports and A,A1, A2, A3 are output ports. In the circuit there are 3 motors. One motor drives the drum and other two drive the capstans. Capstan motors can be connected either in series or parallel depending on the required speed and load using a directional control valve. When the load is less, the motors are connected in series and vice versa when the load is more. There are two sequence valves used in the circuit to control the sequence of fluid into the motors. The flow is initially directed into the drum motor which is followed by the capstan motor irrespective of the influence of resistance. Pressure relief valves are used for safety and the check valve with the drum motor works as a brake so that it restricts the drum from unnecessary rotation. The circuit is a closed loop system with a closed loop variable . The manifold in Fig. 2 has a total of 12 bends. There are 6 branches, 2 offsets, 2 elbows and 2 sudden area changes. All of these constitute to make the hydraulic circuit. The hydraulic manifold has ports to fit in screw-cartridge valves and can connect to pumps and motors.

Fig. 1 Hydraulic circuit of the winch machine

Fig. 2 Three-dimensional CAD model of hydraulic manifold

138 5. Current Methodology A preliminary test is conducted on an elbow bend to compare the CFD analysis results with the semi-empirical equations just to calibrate and validate the accuracy of the results. 5.1 Governing Equations The flow of fluids can be described mathematically using law of continuity and law of momentum. Continuity equation and Momentum equation are the basic equations for the flow of fluids. According to continuity equation, the amount of fluid entering is equal to the amount leaving and according to momentum equation, momentum in the system is balanced. Momentum equation is also called Navier-Stokes equation. For incompressible fluids continuity equation is mentioned in eq. (1) and momentum equation is mentioned in eq. (2). 휕푢/휕푥 + 휕푣/휕푦 + 휕푤/휕푧 = 0 (1) 휕푢 휕푢 휕푢 휕푢 {𝜌 + 𝜌푢 + 𝜌푣 + 𝜌푤 } ∆푥∆푦∆푧 = ∑ 퐹푥 (2) 휕푡 휕푥 휕푦 휕푧 5.2 Computational Fluid Dynamics (CFD) Computational fluid dynamics popularly known as CFD, is used to study the fluid behavior under dynamic conditions. Using computers and numerical analysis, it generates fluid flow simulations to give visual understanding of fluid movements. Results obtained are approximations as it uses numerical methods to solve complex partial differential equations (PDE) over small finite volumes called grids or mesh over the geometric domain. Solutions from this iterative process can solve PDE and determine thermal flow, pressure loss, fluid flow distribution etc. Several applications in the field of aerospace, automobiles, robotics, heavy machinery etc. utilize CFD analysis as their principle software in order to quickly solve complex problems and yield values throughout the mentioned area. Problems that entail cumbersome analytical or experimental approaches can be diminished by using CFD therefore reducing the cost and risky technical difficulties. In this research, complex bends in the manifold are considered which are difficult to solve using analytical methods. Therefore, CFD analysis is used to get the flow properties in order to use it in MATLAB Simulink to evaluate the hydraulic efficiency of the manifold. As CFD gives approximated results, justifying the accuracy of the method and meshing, the results are compared with known theoretically derived empirical equations. 5.3 k-ε Turbulent model The standard k-epsilon (k-ε) turbulence model is the most widely used model in CFD to analyze and simulate the turbulent flow conditions. It is a two-equation turbulence model as it describes the result of conservation equations using two transport equations k and epsilon. This model is an improvement compared to the mixing length model as it has good stability for high Reynolds number [19]. The first transport model k-equation (eq. (3)) arbitrates the energy from the energy equation and is described as turbulent kinetic energy (k). The second transport model is the dissipation of turbulence in eq. (4), which describes the rate at which turbulent kinetic energy dissipates. The experimental form for the standard k-e model can be described as in [20]. The equations that determine the model are: 휕 휇푡,푚 (𝜌푚푘) + 훻. (𝜌푚푣⃗푚푘) = 훻. ( 훻푘) + 퐺푘,푚 − 𝜌푚휀 (3) 휕푡 𝜎푘 휕 휇푡,푚 휀 (𝜌푚휀) + 훻. (𝜌푚푣⃗푚휀) = 훻. ( 훻휀) + (퐶1휀퐺푘,푚 − 퐶2휀𝜌푚휀) (4) 휕푡 𝜎휀 푘 𝜌푚- Mixture density 푣⃗푚- Mixture velocity 휇푡,푚- Turbulent viscosity 퐺푘,푚- Production of turbulence kinetic energy 5.4 Initial and boundary conditions of hydraulic manifold The 2D modelling of the elbow and the CFD analysis is done in ANSYS FLUENT, using the k-ε model in Fig. 3. The computational mesh is simulated considering the following boundary conditions in Table 1.

Table 1 Boundary conditions for computational mesh Initial & Boundary Conditions of Manifold Parameter Values Inlet Velocity 40.2 m/s Diameter of pipe 7mm Flow rate 100LPM Density of fluid 789 kg/m3 Viscosity 8.7 Centi stroke Density of mild steel 7850 kg/m3

139 INLET OUTLET WALL

Fig. 3 Boundary conditions defined for the elbow bend

5.5 Mesh independence study To establish the accuracy of the CFD solution, and to keep the computational time low, the elbow bend was analyzed using the standard k-e model, at uniform velocity of 40.2 m/s. The grid convergence study was performed by changing the mesh size. Initial analysis was made using grid size of 3 mm and has been decreased to 0.03mm. The number of elements, nodes, element size, pressure and pressure difference are given in the Table 2 Y+ values for the model are noted and formulated to Fig. 4; between Y+ values versus the number of Elements. Out of all the iterations, the final iteration results in a near wall resolution i.e. Y+ value is less than 10 by using the standard wall function approach.

Table 2 Iterations for mesh independence study ITERATIONS ELEMENTS NODES SIZE(mm) Y+ P1 P2 DP BAR Iteration 1 760 856 0.8 150 0.74 9.22 8.48 Iteration 2 2044 2205 0.5 80 0.032 8.6 8.6 Iteration 3 4641 4884 0.33 68 0.007 9.95 9.943 Iteration 4 12775 13176 0.2 43 0.0726 10.0 9.92 Iteration 5 51100 5190 0.1 23 0.30 10.3 10.0 Iteration 6 80258 81227 0.08 18.5 0.77 10.74 9.97 Iteration 7 181900 183410 0.053 12.5 0.6 8.2 7.6 Iteration 8 568057 570684 0.03 9 0.6 6.9 6.3

160 140 120 100 80

Y+ Y+ Value 60 40 20 0 0 100000 200000 300000 400000 500000 600000 Elements

Fig. 4 Y+ Values versus number of elements 5.6 Computational Fluid Dynamics (CFD): Preliminary Analysis As we have considered different models of bends in the manifold, inputs to the CFD analysis include system pressure (in bar), a constant value of diameter of the pipe (D in mm), local loss coefficient (k), specific mass (J/kg K), density of the fluid (in kg/m3), gravitational constant (g in m/s2) and type of fluid and flow (Q in LPM and m3/s). The outputs consist of change in pressure P and temperature T through the manifold. 5.7 Empirical Equations for Head Loss in Bends of the Manifold

 v2    hm = k  (5)  2g 

4Q v = (6) D 2

140 P = ghm (7)

hm - Head loss in bends of manifold in Meters (m). k - Constant based on bends. g - Gravitational constant in meters per second square (m/s2) v - Velocity in Meters/Second (m/s). D - Diameter of the pipe in millimeter (mm). Q - Flow rate in Liters/minute (LPM) or cubic meters per second (m3/s). P - Pressure drop (in bar).  - Density of the fluid in kilogram/cubic meter (kg/m3). 5.8 CFD Analysis in Solid Works A 90°-degree bend (elbow) is considered Fig. 5 with diameter of 7mm and the inlet flow rate into the bent pipe is 100LPM. Fluid chosen has density of 789 kg/m3. These conditions are considered for both theoretical calculation and CFD analysis. Fluid enters from one end of the pipe and the other end is open to the atmosphere.

Fig. 5 Flow in the pipe showing the variation of pressure in the bend

5.9 Calculation Empirical calculation for a 90 degrees elbow; using eq. (5), eq. (6) and eq. (7), Diameter = 7mm= 0.007 m, Flow rate = 100 LPM = 0.0016 m3/s, k = 2, Density = 789 kg/m3. 4 * 0.0016 v = = 40.2m / s (6a)  * 0.007 2  40.22    hm = 1  = 82.36m (5a)  2*9.81  P = 789 *9.81*82.36 = 637,473 pa = 6.37bar (7a)

The pressure drop is calculated using empirical equation eq. (5a), eq. (6a) and eq. (7a) is tabulated in Table 3. Value of Pressure drop from the empirical equation is 6.37 bar and the value of pressure drop from CFD analysis in Fig. 3 is 6.3 bar. Therefore, the difference is a value of 0.07 bar.

Table 3 Comparison of Pressure Drop between Practical and Theoretical Calculation Empirical Equation 124952.3 Pascal 6.37 bar CFD Analysis 1119739.5 Pascal 6.3 bar 5.10 CFD and Graphical Analysis of all the Common Bends and Valves in the Manifold In the present research work four types of bends Fig. 6, Fig. 7, Fig. 8, Fig. 9 are considered. A specific working fluid which is used in the cable pulling winch machine is considered as the fluid flowing in the pipe. The parameters varied are flow rate at the inlet and diameter of the pipe to calculate the pressure drop. The pressure drop across the bends is found using CFD analysis. The results are graphically depicted keeping the X axis as flow rate and diameter and Y axis as pressure drop. To plot the diameter versus pressure drop in Fig. 10 for the bends, the diameters considered are 5mm, 7mm, 10mm and 15mm for a constant flow rate of 20 LPM.

141

Fig. 6 CFD analysis of elbow Fig. 7 CFD analysis of sudden area

Fig. 8 CFD analysis of branch Fig. 9 CFD analysis of offset bends

It is observed that the diameters of the pipes and pressure drops are inversely proportional, therefore, as the diameter increases, the pressure drop decreases. It is also observed that; offset bends have the highest-pressure drop-in contrast to others and elbows have the least pressure drop. To plot the pressure drop versus flow graphs in Fig. 11 and Fig. 12 a constant diameter of 10mm is assumed and the graphs are grouped as Elbow & Sudden area change and Branch & Offset with variable flow rates. A common characteristic of the graph noticed is that the flow rate and pressure drops are directly proportional to each other. If the pressure drop is high, the efficiency in eq. (8) of the manifold will be low. The pressure entering the manifold (Pin) from the pump incurs pressure losses in the manifold and thus, the pressure out of the manifold (Pout) will be less. The difference in pressure or pressure drop is Ploss in eq. (9). P (8)  = out Pin

Pout = Pin − Ploss (9) Hence, using all these values, the speed and torque needed for the motor to rotate drum and capstan are also attained. The main objective of the research is to calculate the pressure drop and efficiency of the complete manifold using MATLAB, hence the pressure drop across the valves in the manifold are also considered.

Offset 6.1 Elbow 8.09 SuddenArea Branch SuddenArea 6.09 4.1 Elbow 4.09 2.1

2.09 Pressure Drop (in bar) (in Drop Pressure Diameter (mm) 0.1 Flow Rate (LPM) 0.09 Pressurebar) (in drop 20 40 60 80 100 5 7 10 12

Fig. 10 Pressure drop vs Diameter for common bends Fig. 11 Pressure drop vs Flow rate for Elbow and Sudden area change

1.7 Branch 1.5 Offset 1.3 1.1 0.9 0.7 0.5 0.3

Pressurebar) (in drop Flow Rate (LPM) 0.1 10 20 30 40 50

Fig. 12 Pressure drop vs Flow rate for Branch and Offset bends

142 The major valves integrated are Sequence valve, Pressure-relief valve, Check valve and Directional control valve. The characteristics of the valves are shown in Fig. 13, Fig. 14, Fig. 15(a) and Fig. 14(b). The pressure drop is plotted against the flow rate which is taken in X-axis. These graphs are obtained from the manufacturers’ catalogue.

16 2.5 14 12 2 10 1.5 8 6 1 4

Pressurein bar 0.5

2 Pressure in bar loss 0 0 0 30 60 90 120 0 5 10 15 20 25 Q=Flow=L/min Q=Flow=L/min

Fig. 13 Plot of the characteristics of sequence valve Fig. 14 Characteristics of pressure relief valve

16 14 14 12 12 10 10 8 8 6 6 4 4 Pressurein bar 2 2 0 Pressure loss bar in 0 0 25 50 75 100 0 10 20 30 40 Q=Flow=L/min Q=Flow=L/min

Fig. 15(a,b) Characteristics of directional control valve & check valve in the manifold

6. MATLAB Modeling MATLAB, commonly known as, Matrix Laboratory, developed by MathWorks, is a commercial software in popular demand among design engineers, researchers and programmers in various industrial sectors. It is a numerical-computing software that is integrated with graphical user interface (GUI) and can be programmed simultaneously with languages such as C, C++, Java, Fortan, Python etc. This software is capable of recreating user interfaces, real-time dynamic models, matrix calculations, graphical multi-domain simulations as well as iterating complex mathematical problems. MATLAB Simulink is an additional package with the original software wherein a theoretical design is engineered in the form of graphical diagrammatical blocks that are dragged and dropped into the worksheet from an extensive component library. Generally, these blocks are comprised of pre-defined function blocks and the user is also given the flexibility to design custom blocks. A user-defined function is a function block created according to the user which is then saved as an innate function that can be used for future modeling. Arguments or parameters that majorly define the function block can be scalars, vectors or matrices. These parameters are usually considered to be n number of inputs or outputs. These arguments must be delegated values in order to have an error-free compilation. Inherent one-dimensional lookup tables are basically memory databases where values are stored and retrieved to evade time-consuming computational processes. Hence, this table is used as a reference. A model of the hydraulic manifold is designed in MATLAB Simulink to simulate and test the performance of the manifold. The model includes valves and bends which are constructed using user defined function blocks. For different types of bends, different user defined blocks are made. These blocks consist of one-dimension lookup table which explains the relation between pressure drop and flow for different bends obtained from CFD analysis mentioned in the previous sections. All the user defined blocks have inputs and outputs as flow and pressure. Once, all the user defined blocks are placed as shown in Fig. 16, the hydraulic manifold described in Fig. 2 is replicated. Therefore, all these user defined blocks are placed in a sequence mimicking the hydraulic circuit described in Fig. 1, Hence the winch circuit is simulated in MATLAB Simulink and the efficiency of the hydraulic manifold is calculated.

143

Fig. 16 Two-dimensional layout of hydraulic manifold

The input parameters of the manifold subsystem are shown in Fig. 17. The block include total flow rate Qin and system pressure Psys from the hydraulic pump. The outputs of this subsystem include the pressure and flow rates to the drum motor and capstan motors (Capstan 1 and Capstan 2). The manifold produces sufficient speed and torque from the flow and pressure of the to operate the motors connected to the drum and capstans. The load simulator inputs real-time loads to the motors. The manifold subsystem consists of the offset, elbow and three branch user defined blocks with their respective lookup tables. The blocks require input parameters, specifically the system pressure and total flow rate value.

Fig. 17 Manifold subsystem

The final winch model in Fig. 18 embodies all the user defined blocks for all the components in the machine. It constitutes of the internal combustion (diesel) engine, a hydraulic variable pump, the hydraulic manifold, three bi-directional motors connected to the double capstans and drum, a load simulator and display. The chemical energy from the diesel engine drives the pump that is hydro- mechanically coupled with the manifold. Figure 19 represents the internal setup of the offset subsystem. As an offset bend is divided into mainline and offset line, the inlet flow rate is affected, and different pressure drops are observed. Therefore, a particular user defined block is created for flow division. This block is placed at the division and it calculates the pressure drop in each line. There are only two inputs to this block namely the flow rate in the offset line and flow rate in the mainline respectively. The outputs obtained from the offset subsystem are flow rate and pressure loss across the main line and the offset line. Simultaneously, these outputs are used as inputs for the following Branch subsystem.

144

Fig. 18 User defined function blocks of whole winch system

Fig. 19 User defined function blocks and lookup tables of Offset subsystem

Figure 20 depicts user defined function blocks of branch subsystem. Similarly, the offset and the branch subsystem inputs include mainline flow rate and pressure loss of the offset subsystem. A flow division block is also placed to calculate different pressure drops in mainline and branch line after the split in inlet flow rate. The two inputs to this block include the flow rate in mainline and that of the branch line. Preceding the pressure drop function block in both the offset subsystem and branch subsystem, one- dimensional lookup tables that are pre-defined from graphical values through CFD analysis are created. This block substitutes as the pressure input to the pressure drop function block. Therefore, an accurate pressure loss is calculated.

145

Fig. 20 User defined function blocks and lookup tables of Branch subsystem

Unlike branch and offset, elbow systems in Fig. 21, do not have any split in the geometry of the bend nor does the inlet flow rate gets affected in any way. As it is a straightforward 90⁰ bend, the only region the pressure loss is observed is when the fluid collides with the wall of the bend during the turn. Hence, the elbow subsystem is simplified and designed with one lookup table, a pressure drop function block and inputs of flow and pressure respectively.

Fig. 21 User defined function blocks and lookup tables of Sequence valve subsystem

Therefore, this complete mathematical model simulated in MATLAB will provide the architecture to calculate the efficiency of the manifold and model internal mechanism of the entire cable pulling winch in Fig. 18.

6. Results It is inferred that, the hydraulic components namely the pump, manifold and motors contribute to arrive at the total efficiency of the system ( total ). Therefore, the necessary efficiencies are pump efficiency ( pump ), manifold efficiency ( M ) and motor efficiency (motor ). and motor are provided by the manufacturer.  M is calculated through the current research as the ratio of output pressure from the manifold to the system pressure given as input. The internal roughness that can also contribute to rise in pressure drop is neglected. After analyzing the results of bends from CFD analysis and feeding them into a MATLAB simulated hydraulic manifold algorithm, it is deduced that the manifold can be optimized using this method, and the overall hydraulic efficiency is calculated. It is observed in Fig. 22. that, the efficiency trend line gradually decreases as the flow increases for a given pressure value. Therefore, the efficiency of the manifold continuously varies as it is influenced by the pressure and flow parameter. This in turn affects the overall hydraulic efficiency.

146 86%

100Bar 82% 160Bar

78% 200Bar 240Bar

74% 300Bar Hydraulic Efficiency Hydraulic Flow Rate (LPM) 70% 20 40 60 80 100 120 140 160 180 200

Fig. 22 Hydraulic Efficiency vs Flow rate for different values of pressure

Figure 23(a) illustrates the real time implementation and testing performed to calibrate and generate experimental data that validates the result of overall hydraulic efficiency. The highlighted manifold block consists of multiple nodes through which the hoses and valves are connected from the pump and to the respective motors. The valve is manually adjusted to vary the flow. Figure 23(b) highlights the pressure sensor to depict the proximity of the manifold connections to the rest of the components such as the drum motor, sensors and capstan motors.

Hydraulic Motor Manifold

Pressure Sensor

Fig. 23(a,b) Real time implementation of hydraulic manifold and Proximity of the other components to the manifold

Figure 24 is the display of the software used to realistically test and calculate the pressure loss and overall efficiency of the hydraulic manifold and the complete machine. The pump pressure and flow is set by the operator and the pressure loss is encountered by the drum and capstan motors. Therefore, Table 4 contains the real-time testing values of parameters that influence the overall hydraulic efficiency of the machine and Table 5. Is the comparison between practical and simulated results. These values approve and validate the simulation used to present the analysis in the software.

Fig. 24 Real-time implementation using software to calculate overall efficiency and pressure loss

Table 4 Practical Test values Values Results Pump Pressure(bar) 150 Motor Pressure(bar) 129.14

147 Flow Rate (LPM) 100 LPM Pressure Loss(bar) 20.86 Overall Efficiency (%) 84.18

Table 5 Comparison between practical and simulated test results Values Results Pump Pressure(bar) 150 Flow Rate (LPM) 100 LPM Overall Efficiency (%)-Experimental 84.18 Overall Efficiency (%)- Simulated 86.4

7. Conclusion and Future Scope Optimizing all the components from pumps to motors, valves and manifolds, greatly influence the efficiency of the system as these elements majorly contribute to losses and fuel consumption in a hydraulic system. Using the commercial software of MATLAB and SOLIDWORKS to perform mathematical modeling and CFD analysis, it is observed that the overall hydraulic efficiency fluctuates depending on the flow and pressure values. This elaborated mode of analysis will prove to be a justifying solution to calibrate, validate and to attain results of the efficiency and fuel consumption of the complete machine with the incorporated hydraulic components. As the data obtained from the CFD analysis are particular to this manifold design, in the future with the use of Artificial Neural Networks (ANN) the model can predict the pressure losses of different types of bends with different diameters and different flows in the manifold. Hence, the results acquired can be used for higher level of optimization of the manifold.

Nomenclature

hm Head loss in bends of manifold [m] D Diameter of the pipe [mm] 3 k Constant based on bends Q Flow rate [m /s] g Gravitational constant [m/s2] ∆P Pressure drop [bar] v Velocity [m/s]  Density of the fluid [kg/m3] m Mass [kg] s Specific heat [J/K] m*s Specific Mass [J/kgK] ∆T Temperature [K] 𝜌 Mixture density Mixture velocity 푚 푣⃗푚 휇푡,푚 Turbulent viscosity 퐺 Production of turbulence kinetic energy 푘,푚

References

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