Flow in an elbow with a throttle valve- Steady State with valve fully open

Flow through pipe bend with Butterfly valve.

A Butterfly valve is a quarter-turn rotational motion valve, that is used to stop, regulate, and start flow.

Butterfly valves are easy and fast to open. A 90° rotation of the handle provides a complete closure or opening of the valve. Large Butterfly valves are usually equipped with a so-called gearbox, where the handwheel by gears is connected to the stem. This simplifies the operation of the valve, but at the expense of speed.

Butterfly valves has a short circular body, a round disc, metal-to-metal or soft seats, top and bottom shaft bearings, and a stuffing box. The construction of a Butterfly valve body varies. A commonly used design is the wafer type that fits between two flanges. Another type, the lug wafer design, is held in place between two flanges by bolts that join the two flanges and pass through holes in the valve's outer casing. Butterfly valves are especially well-suited for the handling of large flows of liquids or gases at relatively low pressures and for the handling of slurries or liquids with large amounts of suspended solids.

Typical applications of Butterfly valves

A Butterfly valve can be used in many different fluid services and they perform well in slurry applications. The following are some typical applications of Butterfly valves:

• Cooling water, air, gases, fire protection etc.
• Throttling service involving low differential pressures, as in cooling water or air supply systems.
• Slurry and similar services.
• Vacuum service.
• High-pressure and high-temperature water and steam services.

Advantages of Butterfly valves

• Compact design requires considerably less space, compared to other valves.
• Light in weight.
• Quick operation requires less time to open or close.
• Also available in very large sizes.
• Low-pressure drop and high-pressure recovery.

Disadvantages of Butterfly valves

• Throttling service is limited to low differential pressure.
• Cavitation and choked flow are two potential concerns.
• Disc movement is unguided and affected by flow turbulence.

Domain:

Some Important concept:
Stagnation Pressure: In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure. The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure plus static pressure. Total pressure is also equal to dynamic pressure plus static pressure so, in incompressible flows, stagnation pressure is equal to total pressure. In compressible flows, stagnation pressure is also equal to total pressure provided the fluid entering the stagnation point is brought to rest isentropically. Choked flow: Choked flow is a fluid dynamic condition associated with the venturi effect. When a flowing fluid at a given pressure and temperature passes through a constriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases. At initially subsonic upstream conditions, the conservation of mass principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the constriction. At the same time, the venturi effect causes the static pressure, and therefore the density, to decrease at the constriction. Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment for a fixed upstream pressure and temperature. For homogeneous fluids, the physical point at which the choking occurs for adiabatic conditions, is when the exit plane velocity is at sonic conditions; i.e., at a Mach number of 1.[1][2][3] At choked flow, the mass flow rate can be increased only by increasing density upstream and at the choke point. The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, and depends only on the temperature and pressure and hence the density of the gas on the upstream side of the restriction. Under choked conditions, valves and calibrated orifice plates can be used to produce a desired mass flow rate.
Problem Statement: To simulate and analyse flow in Elbow with Throttle valve or Butterfly valve and mainly check for pressure built-up around the throttle body.

Mesh:
Size: 2e-3mm
Fixed Embedment: two layers with scale of two.

Mesh at 0th cycle fully Open (0 degree)

Mesh at 15000th cycle fully closed (0 degree)

Boundary Conditions:
Inlet: Inflow Pressure: 150000 Pa
Temperature: 300K
Specie: Air (with O2 and N2 at usual concentrations)
Turbulent Kinetic Energy: 0.02% intensity
Turbulent Dissipation: 0.003 m
Outlet: Outflow Pressure: 100000 Pa
Backflow temperature: 300K
Backflow specie: Air (with O2 and N2 at usual concentrations)
Turbulent Kinetic Energy: 0.02% intensity
Turbulent Dissipation: 0.003 m
Elbow Wall: Fixed/ Stationary Wall using law of wall for velocity, temperature.
Throttle Valve/Butterfly Valve: Fixed/Stationary Wall with law of wall used for temperature, velocity.

Solver Details:

Physical Model: RANS- Reynolds Averaged Navier Stokes

Turbulence Model: K-Epsilon RNG

Solver: Steady-State solver, Full Hydrodynamic, Compressible.

Simulation time: 15000 cycles

Initial time step: 1e-9
Minimum time step: 1e-9
Maximum time step: 1.0

Discretisation Schemes:

Navier Stokes Solver Scheme: PISO
Navier Stokes Solver Type: Pressure-Based
Convective Flux Scheme: Flux blending
Specie: Flux blending
Turbulence: Flux blending

Initialization: domain: Air

Pressure: 101325 Pa

Temperature: 300K

Grid Size: 2e-3mm.

Results:

Inferences and conclusion:

• This simulation uses fixed embedment with 2 layer and at scale of 2, this allows refinement of the mesh near the rotating wall (butterfly valve) this allows more fruitful data around this boundary, although this being a steady state simulation no rotation was given to the valve.
• This flow is a pressure driven flow that is high total pressure is defined at the the inlet boundary and the domain is at lower pressure, once the flow starts the total yields higher velocities at inlet.
• In the course of the fluid flow when it encounters the valve which is initially in open position, some high- and low-pressure zones form which can be seen from the following figure.

• The red region shows high pressure of about 1.5e5 Pa and blue region shows low pressure 1e4 Pa, now this pressure is not much of concern because the pressure is not low enough to cause cavitation, moreover the fluid used here is air so there is no threat of cavitation.
• As the valve is fully open there is not much hinderance to the flow so the pressure build up in not much of a concern.

• The above figure shows the pressure contour for the entire domain, which remains mostly the same throughout the simulation.
• Next we see is an image with different view point to understand the pressure built up on the valve surface.
• The red coloured zone has very small area and is not much of a problem.

• The above image shows the velocity contour with arrows depicting the direction of flow, we can see some red coloured arrows toward the bottom and top of the valve, they can actually be ignored because they appear just below the valve where in a reality will be the shaft (stem) on which the valve is mounted.

• Low pressure as we see occurs in a very small region and has a pressure at its lowest of around 54000Pa which would be a matter of concern if the fluid used was some liquid with vapour pressure around this value. But for now, it’s safe.
• Next is an image showing the velocity contour for the domain.

• The velocity rangers from 16m/s to 310m/s which is definitely a wide spectrum, also as discussed earlier the velocities above 250 or 300m/s can be neglected as described earlier.
• From one of the graphs shown earlier we can see the pressure drop across the valve is found around 14489 Pa. Now this drop in pressure across the valve can be accounted by the drop in head due to pipe bend, due to frictional losses in the pipe and various other.
• The most important aspect we are looking for in this simulation is the pressure built up in and around the valve and check for the possibility of cavitation, because we aim to find any such possibility and find out way to avoid it as cavitation is undesirable for any such case of flow through valves.
• For this simulation as air was used as a fluid of flow the possibility of cavitation can be ruled out but if same results were obtained for water or some other liquid then the low pressure regions had to rectified either by improving the design parameters of the valve or by improving the flow characteristics like the inlet total pressure extra.

References:

1. Fluid Mechanics and Hydraulic Machine, Sukumar Pati, IIT Kharagpur- Mechanical Engineering Department.
2. Computational Fluid Dynamics Analysis of Butterfly Valve Performance Factors, Adam Del Toro, Utah State University.