Steady and unsteady

Steady and unsteady

The flows studied in fluid mechanics are divided into two categories, steady flows, and unsteady flows, in terms of the dependence of the flow characteristics on time. In this section, we introduce steady and unsteady flows and mention the reasons that cause the flow to become unstable. Finally, we discuss using Fluent software to simulate steady and unsteady flows.

Steady and unsteady flow

Steady flow refers to a flow in which the characteristics of the flow and fluid are unchanged and constant at a certain point over time. On the other hand, unsteady flow refers to a flow in which the variables of the flow or fluid are variable concerning time at a specific point, and their values change with time. Most of the currents in nature or industry are unsteady, but they can be assumed to be stable by ignoring small changes and time averaging of the flow characteristics.

Changes in environmental conditions, boundary conditions, deformation, displacement, and movement of geometric boundaries can cause the flow to be unsteady. Of course, some flows are inherently unsteady, such as turbulent flows. We know that small and large eddies appear randomly in turbulent flows, and after traveling a distance, they merge or disappear. Therefore, the speed and pressure at any point of the turbulent flow change with time and are not constant. But in many turbulent flows, the flow can be assumed steady and simulated with a suitable approximation. For example, we can refer to Reynolds time averaging turbulence models (RANS) to simulate turbulent flows.

steady & unsteady

unsteady caused by changing environmental conditions

If the environmental parameters change over time in some flows, we will witness an unsteady flow. These changes may be linear, sinusoidal, step, or even random. The movement of waves in the seas and oceans, the movement of air in the lungs, and the sedimentation of solid particles in gas-solid or liquid-solid multiphase flows are three examples of unsteady flows with these characteristics. In such a situation, the computing domain (i.e., spatial grid) remains constant, and there is no need to change the computing domain. Only equations are solved over time, with constant or variable time steps.

Of course, in each time step, solving the governing equations will be repeated. This repetition of solving the equations in each time step should continue until the residuals of the equations reach convergence, and the flow parameters do not change in that time step. Considering the step value, how much we determine the time, these repetitions can be small or large. The larger the time step, the more repetitions are needed to reach convergence.

lung CFD

unsteady caused by the displacement of the boundary condition

Another reason that causes the flow to become unsteady is the displacement of geometric boundaries. If continuous or periodic deformation occurs at the boundary of the walls during fluid movement, then the flow cannot be steady and depends on time. Of course, this phenomenon can be passive (resulting from the forces applied by the fluid to the object, such as the flutter of an airplane wing, or the intermittent deformation of the vessel due to the movement of blood in the area where there is a blockage) or active (a mechanical mechanism, such as low or increasing the fluid pressure inside a balloon or airship cause the change in shape).

In such flows, the computing domain is not fixed and changes continuously. Still, these displacements may be limited only to the deformation of the boundary elements, and the computing domain remains constant in other places. If this is the case, the simulation of this problem can be done more easily and with less computational cost.

airplane flutter

If the walls are moved, such as opening and closing all types of valves, movement of the rudder, aileron, flap, or elevator during the flight of the aircraft; The movement of the piston inside the cylinder and examples like that, the flow also becomes unsteady under the influence of the movement of the walls. The computing domain must be moved and changed near the walls in this situation. This change in the computing network can be in the form of stretching or compressing the elements, production, and loss of elements, or the overall change of the computing network in the whole domain should be with a new grid.

Finally, the flow in a problem that has several separate bodies and the bodies have a relative motion to each other is also unsteady. Such as the flow in a turbine or compressor, considering the movement of the rotor relative to the stator; An object falling into water or a train moving in a tunnel are examples of unsteady flows. To simulate such phenomena, it is necessary to solve the equations governing the movement of objects and the equations governing the flow. For example, in the free movement of objects in three dimensions, solving the kinematic equations defined in 6 degrees of freedom is necessary. It is also essential to solve part of the grid of the computational domain that is moved or generated repeatedly during the grid calculations.


Simulation of steady and unsteady flows using Fluent

In Fluent software, it is possible to simulate both steady and unsteady flow modes. To determine this in Fluent, in the photo shown below, we specify the time mode of the flow by selecting the Steady and Transient options.

fluent 1

The formulation used to solve unsteady flows in the Fluent software differs depending on the pressure base or density base solver used. In the pressure base solver, the discretization of the time terms of the equations is based on the implicit first and second-order methods, as well as the bounded second-order. The convergence and solution process in first-order discretization is faster, and results are more accurate in second-order.

fluent 2

If using the density base solver, if the Explicit formulation is selected as the solution method, then one of the three options Explicit, First Order Implicit, and Second Order Implicit will be available; if the Implicit formulation is used, only the First Order Implicit and Second Order options will be available, and Order Implicit can be selected.

fluent 3