Abstract:- In the current project, we shall study the mass flow rate at the outlet of a hypothetical gate valve for variable levels of lift of the gate disk. Gate valves are machine elements that are commonly used to control the flow of fluids through a long pipe. In construction, a gate valve consists of a circular gate disk (with axis parallel to the direction of water flow) together with a spindle. The spindle connects the gate to the valve handle (wheel) as can be seen in Fig 1.1. The gate can move only in the direction perpendicular to the fluid flow. The objective of this paper is to focus on the CFD analysis on the critical components of Gate Valve with our choice of fluid been water (`H_2 o`) & we will be recording the mass flow rate at the outlet with velocity contours for variable lift position of the disk. The lift distance of the disk will vary from a range of 10mm to 80mm for which we will be performing a parametric study. Our choice of software is ANSYS (Fluent).

Theory__________________________________________________________________________

A gate valve is a type of flow control device that controls the flow of gas, oil, or water. Fig 1.1 shows a typical gate valve and its basic components. Gate valve analysis in the past was performed using experiment methods, which requires a number of types of equipment, a lot of time, funds, and so on. It is not a good way to investigate the flow characteristic of an actual prototype of any valve in a laboratory. Nowadays, due to the fast progress of computer visualization and numerical techniques, it becomes possible to perform such task by using simulation techniques wherein valve performance factors can be obtained by using Computational Fluid Dynamics (CFD) software to simulate the physics of fluid flow in a piping system around a valve. 

                                                                                                                               Fig 1.1:- Gate valve components

Geometry_______________________________________________________________________

We start by importing the pre-modeled Exhaust Port geometry to Spaceclaim, where we will be editing our geometry according to our simulation requirements. We will be running the simulation for a total of 8 cases with variable disk lift & the direction of the disk lift is shown in Fig 2.1. We use the "Move" feature from the design tools to provide lift values for our gate disk. Our geometry is made up of two volumes, the solid volume & the fluid volume though which fluid flow will occur. Since, our area of interest lies in simulating fluid flow through the valve, we will be extracting only the "Fluid Volume" from teh geometry. We use the "Volume Extraction" tool to create two separate regions (solid & volume region) as shown in Fig 2.2. 

                                                                                                                Fig 2.1:- Visualize the disk lift direction by hidding the "bonet".

                                                                                                                Fig 2.2:- Fluid Volume Extraction & extention of fluid flow region  

                                                                                                                Fig 2.3:- Front & Side view of the Disk Plate at Various positions of lift.

Meshing Module________________________________________________________________

The process of discretizing our domain of interest i.e. the geometry into smaller pieces is called mesh generation. Ansys Fluent uses a technique called the "bounding box" method to generate a body-fitted mesh. This is done by creating the smallest size hypothetical box possible that can be used to fit the entire geometry into it. In the meshing module interface, we start by assigning names to our geometry. For our geometry, we have 1 inlet,1 outlet & the rest of the unmarked walls will automatically be assigned as adiabatic walls by Ansys fluent. For all 8 cases, the mesh size will be constant with an element size of 20mm throughout the surface of the geometry. The total number of cells generated was 137234.  

Setting Up The Flow Physics_______________________________________________________

In Ansys Fluent after creating the mesh & assigning the boundaries, the next stage of the process is to set up the simulation parameters. This step involves specifying certain properties to capture the physics of the problem perfectly, such as materials used, simulation time parameters, solver parameters, initial & boundary conditions to solve the Navier Stokes equation which are PDEs, defining body forces, type of fluid flow & species involved.

We start by setting up the Domain, here we will be using a pressure-based steady-state solver with absolute velocity formation. We can justify using a pressure-based solver since the velocity or Mach number at the inlet for all 8 cases will be very low [V = 0.14 m/s]. We will be using a "pressure inlet" with a gauge pressure of 10 pa which translates to V = 0.14 m/s. We also enable the Gravitational force with a magnitude of 9.81 m/s² along the negative Z-axis. Along with the standard PDEs, we will also be solving the turbulence equations (2). For materials, our choice of fluid will be water (H20) with `rho = 998.2 ( (kg)/m^3)`& `mu = 0.001003 (kg·m^(−1)·s^(−1))`. 

The next parameter that we need to set up is the Flow Physics, here we will be navigating to the viscous feature & use an upgraded version of the original K-epsilon (k-ε) turbulence model i.e. the RNG k-epsilon (k-ε) turbulence with scalable wall function in which the magnitudes of two turbulence quantities, the turbulence kinetic energy ‘k’ and its dissipation rate ‘ϵ’, is calculated from transport equations solved simultaneously with those governing equations for capturing better flow physics, we also enable "swirl dominated flow" as we can expect swirling inside the cyclone separator. 

We then navigate to the boundary zone, these are user-defined parameters where we assign the inlet velocity boundary condition as a pressure-based inlet. For all 8 cases, we will be having a pressure inlet of 10 pa which translates to a velocity of 0.14 m/s. The final step includes performing a hybrid initialization & running the simulation for 400-500 iterations until the solutions converge.

`R_e = (rho.V.L)/ (mu)`=> 

Results &  Observations___________________________________________________________

A. Residual Plots

 B. Mass-Flow Rate Plots

C. Velocity Contours

 D. Parametric Study

[The (-ve) value indicates that the fluid flow is exiting the fluid domain through the outlet]

 E. Velocity Streamline Plots

Flow coefficient (`C_v`)

The flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop across a valve or other assembly and the corresponding flow rate. Mathematically the flow coefficient C_v (or flow-capacity rating of the valve) can be expressed as :

where:

Q is the rate of flow (expressed in US gallons per minute)

SG is the specific gravity of the fluid (for water = 1)

ΔP is the pressure drop across the valve (expressed in psi).

Conclusion______________________________________________________________________

We sucessfully performed a parametric study on a hypothetical gate valve with varying disk lift from 10mm to 80mm. The fluid is taken as water at standard conditions. The entry is treated as a pressure inlet with a fixed value of 10 pa for all the cases. At the outlet, we have a reference pressure of value 0 pa. The simulation was run on 4 computing cores and takes around 2 hours for the case 1 (10mm) simulation to complete after which we were able to vary the lift from the parametric table. Effectively, analyzing the mean flow through the valve and in the downstream pipe. From the simulation results we can observe that as the lift of the disk increases the mass flow rate at the outlet of the pipe also increases. The velocity contour images above depicts the area of recirculation occurring after the gate valve as a result of the sudden low-pressure region created after the valve regions. Moreover, there is a spike in the velocity just after the opening of the valve. This can be owed to the equation of continuity i.e. a decrease in the cross-sectional area of the flow causes a proportional increase in the velocity of the fluid. There is a drop in the pressure after the outlet of the gate valve. This is because, Velocity is increased (Law of conservation of energy) & Flow is obstructed by half-open valves.