Unsteady Flow Simulation in Hydraulic Systems

An unsteady flow is one where the parameters change with respect to time. In general, any liquid flow is unsteady. But if a hydraulic system is working at constant boundary conditions, then the parameters of the fluid flow change slowly; thus this flow is considered steady. At the same time, if the parameters of the fluid flow oscillate over time relative to some constant value, then it called quasi-steady flow 1.

In practice, most fluid flows are steady or quasi-steady. Examples of the three flows are presented in Figure 1. Steady flow is presented by a simple pipe. The quasi-steady flow is represented by a sharpened edge channel. The unsteady flow is presented by an outflow from a reservoir.

Figure 1 - Different Types of Fluid Flow
Figure 1 – Different Types of Fluid Flow
Different Cases of Unsteady Flow

During operations, hydraulic systems act for long intervals at steady conditions which are called operating modes. Change between two different operating modes occurs over a short time interval (called a transient mode). If any hydraulic system works more than 95% of the time at these operating modes though, why is the unsteady flow is so important? Because the loads depend on time intervals. If the load is less, then the maximum system pressure is higher.

The controls of hydraulic systems are designed to control the time interval of the transient modes to stay within the safe range. But engineers must consider the worst-case scenario of an acting system. The worst case for any hydraulic system is the fluid flow suddenly stopping. In this case the maximum pressure in the channel is at its highest and linearly depends on the density of the fluid, velocity of the operating mode, and sound velocity of the fluid2. This transient mode is called water hammer Figure 2.

Figure 2 – Process of Water Hammer and Typical Damages 3,4

Another type of unsteady flow is created using hydraulic automatics which move actuators. For example, if the rod of a hydraulic cylinder suddenly meets an obstacle when a piston brakes the fluid. The fluctuation in pressure is compensated by check valves 5 and commentators 6.

The Unsteady Flow in in Various Fields of Technology

Unsteady flow is a primary method for several applications. For example, the brake systems for any type of the vehicle (automobiles, freight cars, trans, airplanes) uses short interval time modes to move actuators. In this case, the effectiveness of the hydraulic system depends on the value of acceleration of the fluid. The water hammer is significantly less because the total mass of the fluid is moderate. To decrease the value of a peak pressure, a gas can be used as a working fluid. For example, the fluid used in a train brake system is air with a mass density much lower than that of a liquid 7.

In the energy production branch of gas turbine systems, the dangerous of the water hammer is very small. In these installations, several basic types of a hydraulic systems are used such as lubrication, fuel and control systems 8. The unsteady flow is the most interesting at the start mode9, but it isn’t critically vital nor hazardous.

In aviation and rocketry fields, water hammer is extremely dangerous due to its ability to fracture a fuel pipeline system. The destruction of this type of a hydraulic system happens at the preparation stage in the fueling process 10 or during an operation mode 11.  It’s especially important to note the possibility of the water hammer in the fuel pipeline of a reusable rocket system where on-off cycles switch several times during the flight 12,13(see Figure 3).

Test Program which Include Predicting Potentially Catastrophic Events such as LOX Geyser or Water Hammer
Figure 3 – Sierra Utilizes the Rocket Engine Transient Test Program which Include Predicting Potentially Catastrophic Events such as LOX Geyser or Water Hammer 13
Simulation of an Unsteady Flow at the Stop of the Work Fuel System

The best tool to analyze the processes in any hydraulic system during an unsteady flow is AxSTREAM NET™. The simulation of the LOX system of the rocket engine is considered. Figure 4 shows the model of supply liquid oxygen pipeline of the V-2 fuel system 14,15 in AxSTREAM NET™ and the result of the operating mode simulation. One of the features of this model is imaging of several pipelines as one branch to supply LOX to the injectors of the combustion chamber. As a result, the solver calculated a simulation using several timeless resources to accurately model the flow.

To simulate an unsteady regime the upper part (before the pump) of pipeline was chosen.  In this section, the liquid rams the pump as it suddenly stops and the pressure value abruptly increases.

Figure 4 - Supply Liquid Oxygen Pipeline of the V-2 Fuel System
Figure 4 – Supply Liquid Oxygen Pipeline of the V-2 Fuel System

In the unsteady flow example, an abrupt stop in a pump was considered. This is the worst-case scenario. In fact, for the worse case the stop occurs during some nonzero time. The result of this simulation is shown below in the video. The maximum pressure value is above 2000 kPa which is in 10 times more than the initial one.

Figure 5 – Depending Static Pressure in Pipeline of LOX Before Abrupt Stop of Pump

The worst case of unsteady flow is a water hammer. The pressure increases very quickly which can destroy the continuity of a pipeline wall. Another case of an unsteady flow is a hydraulic automatic system where timing of the processes is very important. The actuator must act rapidly and be saved. In both these cases, an analysis of the hydraulic system is needed.  AxSTREAM NET™ can help you perform these necessary analyses.


1: Meinhard T. Schobeiri, Fluid Mechanics for Engineers: A Graduate Textbook, 2010

2: John A.Fox, Hydraulic Analysis of Unsteady Flow in Pipe, 1977

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8: Claire Soares, Gas Turbines: A Handbook of Air, Land and Sea Applications, 2015

9: Babak Afzali, Hassan Karimi, Ehsan Tahmasebi, Dynamic simulation of gas turbine supply during transient operations, June 14-18, 2010, Glasgow, UK

10: Xiang Youhuan, Zhang Ping, Zhang Hui and Bai Fengtian, Numerical Analysis on Water Hammer Characteristics of Rocket Propellant Filling Pipeline, 2015

11: Avanish Kumarn, P. Satya Prasad, M. Raghavendra Rao, Experimental studies of water hammer in propellant feed system of reaction control system, March 2016

12: Traudt, T.; Bombardieri, C.; Manfletti, C., Influences on water-hammer wave shape: an experimental study, 2016 Sep

13: Sierra Engineering generates computer models that accurately predict and validate engine components and fluid properties., http://sierraengineering.com/LiquidSim/liquidSim.html [2019 Oct]

14: V2 Rocket Engine Question, https://forum.nasaspaceflight.com/index.php?topic=46952.0 [2019 Oct]

15: A-4/V-2 Makeup – Tech Data & Markings, http://www.v2rocket.com/start/makeup/design.html [2019 Oct]