# Mass Flow vs. Delta_P in a CFD Analysis May 8, 2015 By: Hsin-Hua Tsuei

In a CFD analysis, we often use either mass flow rate or inlet pressure (total or static) when specifying boundary conditions at a flow inlet. At the exit, specification of back pressure (static) is the norm, representing a wide range of exit conditions, such as the ambient condition for external flow, and a known pressure data point for an internal flow analysis. One of the most frequently asked CFD questions is: can both mass flow rate and total pressure be specified at the inlet? This question brings some interesting observations.

If I had to guess the origin of this question, I would say that it probably came from engineers reviewing test data.  Imagine you are testing a compressor. At the inlet, both the mass flow rate and pressure are measured, and included in the data. The test stand generally exhausts to ambient conditions.  Since measured mass flow rate and pressure data is available at the inlet, the natural inclination is to presume they are accurate and specify them both as boundary conditions for the CFD analysis. So, can we do this at the inlet boundary? Simply put, no. CFD solvers do not permit specifying both mass flow rate AND pressure at the same location, through user interface face, text input, or any other back door methods. But why? The test data certainly implies that you can.

Let’s first take a look at using the mass flow rate at the inlet boundary. We will use the back pressure (Pb) as the exit boundary condition. By assigning a mass flow rate at inlet, we are “pushing” this much mass through the flow system. The flow passages have no choice but to respond to the requirement, based on the flow path configuration, to arrive at an inlet pressure.  Keep in mind the inlet pressure (P-inlet) is not specified in this situation, but will be calculated as part of the CFD solution. In other words, the flow system is telling us if you want to force this much flow through this particular path, this is the pressure difference you need (P_inlet – Pb). For example, it takes a lot less pressure to pass 1.0 kg/s of air through a large diameter straight pipe than a tight gap. A narrow flow path presents a much higher resistance to the incoming flow, which therefore requires a stronger pressure gradient to get the fixed amount of mass flow through. If a larger amount of mass flow is specified at the inlet, the required inlet pressure is higher and the pressure gradient is larger.

Alternatively, specifying pressure at both the inlet and exit means the pressure difference is fixed for the flow system.  In this situation, the mass flow rate is a result of the specified pressure gradient. For example, a fixed pressure gradient is able to pass a larger amount of mass flow through a large diameter straight pipe than a tight gap. In this situation, the mass flow is not specified at the inlet, but is a calculated quantity derived from the prescribed pressure gradient of the flow system. This means if we want to increase the mass flow, we need a higher pressure gradient.

So, while it is possible to measure mass flow rate and pressure anywhere in the system, we must understand that these quantities are not independent of each other, and therefore cannot be specified simultaneously as boundary conditions to a CFD analysis. However, the measurements can certainly be used to see if the CFD results are correct. For example, if you are specifying inlet mass flow rate in the CFD analysis, the CFD results will include the inlet pressure. If this computed inlet pressure does not match the measured inlet pressure, then something went wrong – either with the CFD analysis, or with the test measurements. The common assumption is that the CFD results are in error, but many times it is the test data. A good check on instrumentation is to check the flow rate at the inlet and outlet. For a closed system, operating at steady state, the mass flow rate at both locations better be the same.  If not, then there is a serious instrumentation error in the test apparatus.

If you know the mass flow rate and the pressure at the inlet, you can use the inlet pressure and specified mass flow rate at the outlet as boundary conditions. The opposite approach will also work – inlet mass flow rate and outlet pressure. Using either of these approaches will allow the CFD analysis to calculate the pressure gradient for you. On the other hand, if you know the pressure at the inlet and outlet, you can specify those quantities as boundary conditions, and the CFD solution will compute the mass flow rate. If the boundary conditions are consistent, all of these approaches will yield the same result.