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Flow Coefficient Analysis for a Globe Valve by using CFD

The valve selections criteria involves determination of valve coefficient, flow characteristics, shutoff requirements, body end connections, pressure classes, face to face dimensions, body and trim material selections, gasket and packing selection and process flow parameters. The measurement commonly applied to the valves is the valve coefficient (Cv) which is also known as flow coefficient. When selecting a valve for a particular application, the Cv is used to determine the valve size that will best allow the valve to pass the required flow rate, while providing stable control of the process fluid. This paper presents the research of Flow Coefficient analysis for a Globe Valve by using Computational Fluid Dynamics (CFD).The globe valve is the most commonly found control valve in the process industry due to its simple design, versatility of application, ease of maintenance and ability to handle a wide range of pressures and temperatures. Globe valves are used in both gas and liquid services. The flow system with Globe valve is complex structure and has nonlinear characteristics. In this paper, three-dimensional numerical simulations and experiment were conducted to observe the flow pattern and to measure valve flow coefficient and flow fluctuations when globe valve with different flow rate and uniform incoming velocities were used in a pipeline system. These results not only provide user with the access of understanding the flow pattern of the Globe valve with different flow rate and velocities, but also were made to determine the methods which could be adopted to improve the performance of the valve.


Introduction
The Control Valve plays a very important part in the automatic control of modern plants, which depend on the correct distribution and control of flowing liquids or gases. Such control, weather for the exchange of energy, reduction of pressure, or simple to fill a tank, depends on some form of Final control element to do the job.
A control valve functions as a variable resistance in a pipeline. It provides a pressure drop by changing the turbulence in the process fluid or, in the case of laminar flow, the pressure drop is caused by the changed valve resistance or drag. This pressure drop process is often called throttling. A control valve is the most important single element in any fluid handling systems, because it regulates the flow of fluid to the process.
By definition, a globe valve is a linear-motion valve characterized by a globe style body with a long face to face dimension that accommodates smooth, rounded flow passages [4]. The advantages of globe valves are manyhence their overall popularity. Generally, globe valve are quite versatile and can be used in a wide variety of services. The same valve can be used in dozens of different applications as long as the pressure and temperature limits are not exceeded. This versatility allows for reduction in spare parts inventory and maintenance training. Their simple linear motion design permits a wider range of modifications than other valve styles [1].
Because of the linear motion, the force generated by the actuator or actuation system is transferred directly to the regulating element; therefore, a minimal amount of the energy to the regulating element is lost. On the other hand, rotary valves lose some transfer energy and accuracy because of the dead band associated with linear-to rotarymotion linkage. For this reason, globe valves are capable of high performance and are used in applications were such performance is mandatory.
A major advantage to using globe control valves is their ability to withstand process extremes. They are designed to work in extremely high pressure drops, handling pressure differentials of thousands of pounds of pressure. Steady flow of a Newtonian, incompressible fluid was assumed. The governing equations were solved using the SIMPLE algorithm [1].
Parts of Typical Globe Valve are: 1) Body is main pressure containing structure and it contains of all of the valves' internal parts. 2) Bonnet provides leak-proof closure for valve body. 3) Disc is closure member of the valve. 4) Stem servers as a connector from the actuator.

Incompressible Flow
When the fluid density does not change with changes in pressure, the fluid is incompressible. Water density changes very little with changes in pressure and is generally treated as an incompressible fluid.
Air is compressible, but if pressure changes are small in comparison with some nominal value, the corresponding changes in density are small also and incompressible quations work quite well in describing the flow. The degree to which the fluid density changes with pressure is related to the speed of sound in the fluid. Thus, assuming that the flow is incompressible is equivalent to assuming that the speed of sound is infinite. When the local Mach number is less than 0.2 to 0.5 compressibility effects can often be ignored.

Flow Coefficient.
The valve flow coefficient is an inherent parameter which measures the valve capacity. It depends on valve type, diameter of valve, opening rate of valve and operating fluids. Cv is defined as the floe in cubic meter per hour of water at a temperature 5-40°C with a pressure drop across the valve of 1 bar.
Where q is the volume flow rate in m3/hr P1 and P2 are inlet and outlet pressures Gf is the specific gravity Correction Factor, Fp=1 Numerical Constant, N1 = 0.862 The valve characteristic is a plot of the Cv versus percentage opening of the valve. The plot is indicative of how the flow rate will change with a change in percentage opening of the valve.

CFD
Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically the set of governing mathematical equations. [1] Philip L.Skousen, Revised to include details on the latest technologies, Valve Handbook, Third Edition, discusses design, performance, selection, operation, and application. This updated resource features a new chapter on the green technology currently employed by the valve industry, as well as an overview of the major environmental global standards that process plants are expected to meet. The book also contains new information on: valves used in the wastewater industry, applying emergency shutdown (ESO) valves.

Literature survey
[2] Qin Yang, Zhiguo Zhang, presents the researches of the authors in modeling and simulation of the stop valves. The flow system with stop valves is complex structure and has non-linear characteristics, because the construction and the hydraulic phenomena are associated of stop valves. In this paper, three dimensional numerical simulations were conducted to observe the flow patterns and to measure valve flow coefficient and flow fluctuations when stop valve with different flow rate and uniform incoming velocity were used in a valve system. The spectra characteristics of pressure fluctuation on the flow cross section were also presented here to investigate the wake induce of the valve part.
[3] Romil Khowal, presents an experimental method to calculate the flow coefficient value of the valve, but the setup for the experimental validation is not readily available as these valves work at high pressure. This paper compares the flow coefficient value at different openings of the valve calculated by ANSYS Fluent 14.5 with the experimental values. The purpose of this paper is to define the boundary condition for the CFD analysis of the valve and to reduce the experimental validation for different sizes and openings and hence reducing the overall expense.
[4] Alexandre Joel Chorin, presents a finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions.
[5] Martin Burg, lecture is to give an overview on modern numerical methods for the computation of incompressible flows. They start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes problem, a linear saddle-point problem, then proceed to stationary Navier Stokes, which adds the complication of a nonlinear equation, and finally discuss the in stationary Navier-Stokes equations, which adds time discretization. In all cases, we shall discuss modern discretization strategies, their major properties, and the solution of the discretized equations.
[6] Benjamin Seibold, presented a simple numerical method for solving the Navier-Stokes equations. It contains fundamental components, such as discretization on a staggered grid, an implicit viscosity step, a projection step, as well as the visualization of the solution over time.
[7] P Howard, provided Partial Differential Equations in Mat Lab. This hand book is intended to acquaint engineers with the factor of control valve design and application and to assist instrument engineers in the selection of the best valve body, actuator and accessories of application.
[9] Howard C. Elman, IFISS is a graphical Matlab package for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions. The package can also be used as a computational laboratory for experimenting with state-of-the art preconditioned iterative solvers for the discrete linear equation systems that arise in incompressible flow modeling.
A unique feature of the package is its comprehensive nature; for each problem addressed, it enables the study of discretization and iterative solution algorithms as well as the interaction between the two and the resulting effect on overall efficiency.  [10] Arkelyan Erik, In the following paper they consider Navier-Stokes problem and it's interpretation by hyperbolic waves, focusing on wave propagation. We will begin with solution for linear waves, then present problem for non-linear waves. Later we will derive for numerical solution using PDE's. Also we will design a Matlab program to solve and simulate wave propagation.

Governing Equations
The actual pressure drop ΔP is calculated using the Cv equation for liquid [11].
Chocked flow can be checked by finding the liquid pressure recovery factor F L which is 0.90. Then the liquid critical pressure ration factor (F F ) is calculated by using the equation.
Where P V = Vapor pressure P C = Critical pressure After determining F L and F F these numbers are used in the chocked pressure drop. A comparison should be made between the actual pressure drop and chocked pressure drop.
ΔP cavitation = F L 2 (P 1 -P V ) In this case actual pressure drop is greater than the pressure drop associated with incipient cavitation. This can be interpreted to mean that, although cavitation is occurring in the service, the cavitation is not causing the flow to chock.

Equations of Fluid Flow
The conservation laws of energy can be used in the analysis of flowing fluids.
The Bernoulli's equation can be considered to be a statement of the conservation of energy principal appropriate for flowing fluids. It is one of the most important equations in fluid mechanics. It outs into a relation pressure and velocity in an inviscid incompressible flow [6].
The general energy equation is simplified to: (4) Where h = height above reference level (m) v = average velocity of fluid (m/s) p = pressure of fluid (Pa) g = acceleration due to gravity (m/s2)

Navier-Stokes equation
A finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Essentially it constitutes an extension to time dependent problems of the artificial compressibility method introduced in for steady flow problems [8].
The equations to be solved can be written in the dimensionless form [8] (5) Where u i are the velocity components, E i the external forces, p is the pressure, and R the Reynolds number, δ i denotes differentiation with respect to the space variable x i , and dt differentiation with respect to the time.
Problem where the velocities or their derivatives are prescribed at the boundary or where some boundary conditions are replaced by periodicity conditions have been investigated. For simplicity, we shall describe the case where the velocities are given at the boundary and shall assume that a Cartesian coordinate system is used. An important feature of the method is the use of equation (2)

Results & Discussions
The Analysis is run for ten opening conditions. The results of the same is listed in the below table.

Conclusion
The modeling methodology for the Flow Coefficient estimation for a Globe valve has been systematically investigated by considering flow parameters. The conclusions are drawn as follows: a) The variation in experimental value and the value from numerical method is about 14.51%. In general practice up to 20% variation is considered. b) The boundary conditions used in this paper are within permissible limits. c) The numerical model values have a good agreement with those obtained by Experimental values, thereby supporting the validity of this approach.

Future Scope
The work covered in the thesis tries to solve Flow coefficient for a globe valve. Still there are some problems are left and are of interest were identified and are mentioned below: Two problems with control valves are found at a high frequency in poorly performing control loops. These are:  Dead band  Stiction

Deadband
For a control valves, deadband refers to a range of controller signal that fails to trigger any activity of the valve. Deadband happens when the valve needs to change direction.
To compensate for deadband, the controller must send additional output, which can cause the valve to overshoot its target position. This in turn causes the process to overshoot its set point.
There are several consequences of high deadband:  Increased dead time  More errors from load disturbances  Higher possibility of rupturing pressure relief discs or vessels  More oscillations in the control loop  Increased control variance

Stiction
Another very common problem found in control loops is stiction. This is short for Static Friction, and means that the valve internals are sticky.
If a valve with stiction stops moving, it tends to stick in that position. Then additional force is required to overcome the stiction. The controller continues to change its output while the valve continues to stick in position. Additional pressure mounts in the actuator. If enough pressure builds up to overcome the static friction, the valve breaks free. The valve movement quickly absorbs the excess in pressure, and often the valve overshoots its target position. After this, the valve movement stops and the valve sticks in the new position.
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Acknowledgement
Our sincere thanks to Mr. Javed A. Hawa, Managing Director of Hawa Valves India Pvt. Ltd. who encouraged and allowed to present this paper.
We also thank Mr. Chitta Nageswara Rao, (M.Tech, and M.B.A) for motivating and providing guidance.