In this week’s post we investigated the possibilities connected to using the transient solver in Simcenter Flomaster and look closer at how to set this up for incompressible transient cases.
Simcenter Flomaster’s Incompressible Transient modelling provides the capability to model time dependent events in a real flow situation with the use of many types of system components. Some examples where this may prove useful involve investigating start-up and trip events for pumps, evaluating the dynamics of control valves, verifying surge protection measures, or simulating the filling and drainage in tanks.
Understanding how quickly or slowly an event occurs within an internal flow system is important when determining how to configure a transient simulation. As sudden, or very fast, events require more consideration compared to slower events we will focus more on these throughout this post. Flow dynamics resulting from gradual changes in valve openings, slow temperature-increase through controlled heat addition, or the steady increase/decrease in pump speed, are all examples of slower transient events. These are naturally important investigations when designing your system, as well as when studying the dynamic behavior during operation. However, equally important is the study of fast transients in internal flow systems.
Fast Transient Pressure Validation (1) C.S. Martin. Sample System validation model in Simcenter Flomaster
Pressure surge in pipes, also known as water hammer, is a special fast transient flow case. Surge analysis is concerned with dynamically changing flow velocities in a pipe, and any system containing liquid in motion will experience some degree of pressure surge. The effect is caused by sudden or rapid flow disturbances, such as liquid flow abruptly stopping due to a too sudden valve closing. This then leads to an excessive pressure rise of the fluid at the location of the disturbance, which in turn propagates out throughout the fluid in the form of pressure waves.
According to the Joukowsky formulation, which relates the instantaneous change in pressure (dP) to an instantaneous change in flow velocity (dv), the maximum pressure rise occurring at the place of the flow disturbance within a confined liquid is directly proportional to the wave speed of which pressure waves travel along a pipe multiplied by the change in flow velocity. As pressure waves can travel above 1200 [m/s] in steel pipes it is clear why this must be properly analyzed in order to avoid pipe ruptures or equipment failure. Note that the wave speed used below is the combined value for both the fluid and the pipe.
The Joukowsky formulation is a simple yet useful method for approximating the magnitude of the instantaneous pressure rise, however the approach is not always necessarily conservative and generally only applicable to a limited set of fluid systems. Some of the limitations involve:
- Only straight pipe systems and no accounting for wave reflection, i.e. no branches, flow splits or bends where pressure waves can be travel back and influence the main pressure wave.
- Uniform pipe properties, such as friction, constant diameter and wall thickness
- No cavitation or release of air
- No consideration for column separation, i.e. pressures below the fluid vapor pressure separating two bulk flows.
- No accounting for other components, e.g. pumps, valves.
To carry out a more complete transient surge analysis with Simcenter Flomaster we will have a look at the concept of classifying events based on how quickly they take place. This approach helps us determine how to configure a simulation for a transient run and guides us in whether simplifications can be made or not. The classifications depend on the relationship between the following:
- The time (t [s]) it takes to complete the change in flow velocity, e.g. time to completely close a valve.
- The pipeline period T [s], which states the time it takes for a pressure wave to propagate from its origin to a point of reflection and then return. T = 2L/a, here L is the length of the pipe [m] and a the wave speed throughout the pipe [m/s].
t > 500 T. An event is classified as a very slow event if the change in flow occurs during a period of time that is larger than 500 T (pipeline periods). In a very slow event, the pressure rise is significantly less dependent on wave speed and more dependent on the velocities rate of change. In these situations it is worth considering using the simpler Rigid pipe models due to the significant increase in computing speed compared to using Elastic pipe components. Additionally, the wave speed does not have to be determined and specified.
1T < t > 500T. A slow event occurs between 1 to 500 T (pipeline periods).
t < 1 T. A rapid event takes place in less than 1 T. In these situations, the pipes have to be modelled using the Elastic pipe components to account for the pressure waves and flow fluctuations within the length of pipe. The elasticity of the fluid and the pipe are accounted for by a combined speed of sound for both fluid and pipe, and pressure waves travel through the pipe at the speed of sound. The passage of these waves is calculated using the Method of Characteristics since the timing of wave reflections and combinations of these can be important for the transient behavior throughout an interconnected system.
To calculate the aggregated wave speed resulting from the combination of liquid and pipe material, the pipe wave speed wizard may prove useful. If an incompressible elastic pipe is selected, the wizard can be found next to the input field for wave speed. For Rigid pipes no information regarding wave speeds is required.
Built in wizard for quickly specifying wave speed for components having different material properties. To properly determine the liquid’s bulk modulus and pipe material modulus engineering tables and diagrams are typically consulted.
When predicting severe pressure surges in an interconnected system containing more than just straight pipes, elastic pipes are used which rely on a computational approach called method of characteristics to correctly track wave propagation throughout the system. To achieve this, pipes in a system have to be discretized with higher resolution, i.e. adding more computational nodes, to form a computational mesh sufficient for capturing the wave propagation during each time-step.
In order to correctly determine how fine or course the mesh needs to be for all elastic pipes contained within the model, the relationship between the pipe length (L) [m], the combined wave speed (a)[m/s] and advancing time/time-step the solver makes, is used. The term reach length (S)[m] denotes how far away computational nodes should be placed from each other within the pipes. An analogy to CFD and its CFL number used in transient simulation can also be made. Here, a sufficiently fine mesh is also required to ensure that no information loss occurs between each time-steps during a transient simulation. Making it important to find a good balance between time-step size and cell size.
In Simcenter Flomaster a value greater than 3 (default value 5) is required for the reach length else an error flag is raised. To ensure that this criteria is met, and to avoid computational instabilities, a user may make smaller adjustments to the length of the pipes, make minor adjustments to the wave speed, and set an appropriate time-step.
The connection between reach length and number of internal nodes is given by the expression below.
To assist with the process of configuring the simulation time-step, the time-step wizard should be used. In this tool, the number of desired reach lengths is specified along with others such as, converge criteria, maximum number of nodes, and allowed difference in wave speed. Once done the wizard will then suggest appropriate time-step and the different wave speeds for all elastic pipes within the system.
Hopefully this text has clarified some of what is involved in setting up and running transient simulations in Simcenter Flomaster and gives you some ideas to help you in your simulation work.
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Author
Fabian Hasselby, M.sc.
