# ACU-T: 5200 Rigid-Body Dynamics of a Check Valve

This tutorial provides the instructions for setting up, solving, and viewing results for a simulation of the opening of a pressure check valve. In this simulation, AcuSolve is used to compute the forces on the valve due to the time-varying inlet flow field and to compute the motion of the valve that results from these flow forces. This tutorial is designed to introduce you to a number of modeling concepts necessary to perform simulations of rigid-body dynamics.

## Prerequisites

Prior to starting this tutorial, you should have already run through the introductory tutorial, ACU-T: 1000 Basic Flow Set Up, and have a basic understanding of HyperMesh CFD and AcuSolve. To run this simulation, you will need access to a licensed version of HyperMesh CFD and AcuSolve.

## Problem Description

The problem to be addressed in this tutorial is shown schematically in Figure 1. It consists of a cylindrical pipe containing water that flows past a check valve with a shutter attached to a virtual spring (not included in the geometry). The inlet pressure varies over time and the movement of the shutter will be determined as a function of the balance of the fluid forces against the reactive force of the spring. The problem is rotationally periodic at 30° increments about the longitudinal axis, and it is assumed that the resulting flow is also rotationally periodic, allowing for modeling with the use of a wedge-shaped section. For this tutorial, a 30° section of the geometry is modeled, as shown in the figure. Modeling a portion of an rotationally periodic geometry leads to reduced computation time while still providing an accurate solution.

The pipe has an inlet diameter of 0.08 m, and is 0.3 m long. The check-valve assembly is 0.085 m downstream of the inlet. It consists of a plate 0.005 m thick with a centered orifice 0.044 m in diameter and a shutter with an initial position 0.005 m from the opening, simulating a nearly closed condition. The shutter plate is 0.05 m in diameter and 0.005 m thick. The shutter plate is attached to a stem 0.03 m long and 0.01 m in diameter. The mass of the shutter and stem is 0.2 kg and its motion is affected by a virtual spring with a stiffness of 2162 N/m. The motion of the valve shutter is limited by a stop mounted on a perforated plate downstream of the shutter.

Note that AcuSolve's internal rigid-body-dynamics solver is not able to simulate contact. Therefore, this problem is formulated to avoid contact between the valve and the stop.

^{1}/

_{12}of the rigid body is modeled, the forces computed by AcuSolve that act on the valve shutter represent

^{1}/

_{12}of the actual force on the device. Therefore, it is also necessary to account for this in the simulation. There are two methods that can be used to accomplish this:

- Scale up the fluid forces calculated by AcuSolve
by a factor of 12 to represent the full load on the device when the
displacement of the body is computed.
Using this approach, the full stiffness of the valve spring is used in the rigid-body solution, and the full mass of the valve is used.

- Scale down the mass of the valve and the stiffness of the spring to by a
factor of 12 to match the fraction of the valve geometry to be modeled.
Using this approach, the loading passed to the rigid-body solver is not scaled.

This second approach is used in this tutorial; the scaled mass of 0.0167 kg and the scaled stiffness of 180.1667 N/m will be used .

The fluid in this problem is water, which has a density
(ρ) of 1000 kg/m^{3} and a molecular viscosity (μ) of
1 X 10^{-3} kg/m-sec.

At the start of the simulation the flow field is stationary. Flow is driven by the pressure at the inlet, which varies over time as a piecewise linear function shown in Figure 2. As the pressure at the inlet rises, the flow will accelerate as the valve opens. The turbulence viscosity ratio is assumed to be 10.

Prior simulations of this geometry indicate that the average velocity at the inlet reaches a maximum of 0.9 m/s. At this velocity, the Reynolds number for the flow is 72,000. When the Reynolds number is above 4,000, it is generally accepted that flow should be modeled as turbulent.

Note that the initial conditions of the flow are actually laminar, however, the increase in flow velocity and flow around the valve shutter is expected to cause a rapid transition to turbulent conditions. Therefore, the simulation will be set up to model transient, turbulent flow. When performing a transient analysis, convergence is achieved at every time step based on the defined stagger criteria. Mesh motion will be modeled using arbitrary mesh movement (arbitrary Lagrangian-Eulerian mesh motion).

For this case, the transient behavior of interest occurs in the time it takes for the pressure to ramp up and ramp back down, which is given by the transient pressure profile. To allow time for the spring to recover, additional time will be simulated. For this tutorial, 0.1 s is added after the pressure drops back to initial conditions, for a total duration of 0.35 s.

Another critical decision in a transient simulation is choosing the time increment. The time increment is the change in time during a given time step of the simulation. It is important to choose a time increment that is short enough to capture the changes in flow properties of interest, but does not require unnecessary computation time.

The change in inlet pressure from initial conditions to maximum occurs over 0.048 s. A time increment of 0.002 s would allow for excellent resolution of the transient changes, without requiring excessive computational time.

## Start HyperMesh CFD and Create the HyperMesh Model Database

## Import and Validate the Geometry

### Import the Geometry

### Validate the Geometry

## Set Up Flow

### Set Up the Simulation Parameters and Solver Settings

### Create a Multiplier Function for the Inlet Pressure

### Assign Material Properties

### Define Flow Boundary Conditions

## Set Up Motion

In this step, you will activate the mesh motion and define the rigid body motion for the valve wall. Then, you will define the mesh displacement boundary conditions for the symmetry surfaces.

### Define the Mesh Motion Type

### Define Rigid Body Motion

### Define the Mesh Displacement Boundary Conditions

## Generate the Mesh

In this step, you will define the mesh controls and then generate the mesh.

### Define the Zone Mesh Controls

### Define the Boundary Layer Controls

### Generate the Mesh

## Compute the Solution

### Define Nodal Outputs

### Launch AcuSolve

### Monitor Results

## Post-Process the Results with HM-CFD Post

### Create an Animation of Velocity Magnitude

### Display Pressure Contours and Velocity Vectors on a Section Cut

## Summary

In this tutorial, you learned how to set up and solve a CFD simulation involving rigid body mesh motion. You started by importing geometry, then defined the flow set up. Next, you defined the mesh motion set up and then generated the mesh. Once the solution was computed, you post-processed the results using the Plot tool and HyperMesh CFD Post.