Turbomachinery Flow Coefficient
Key Takeaways

Turbomachinery flow coefficient is a dimensionless parameter that indicates the efficiency of the turbomachine.

The efficiency is dependent on machine geometry, flow regime, fluid properties, pressure differentials, and operating conditions.

CFD uses the NavierStokes equation to solve for the flow motion and turbomachinery flow coefficient. The result helps in identifying the need for optimization.
Simulating flow in turbomachinery
What is the mechanism for marine or aircraft propulsion? How does a steam turbine or gas turbine work? The answer to these questions can be found through the understanding of the term turbomachinery.
Turbomachinery refers to the machines that ensure the continual transfer of energy between the fluid and the rotor. This includes the turbine, which converts fluid energy to mechanical energy, and compressors, which serve the opposite function.
Turbomachinery refers to the machines that ensure the continual transfer of energy between the fluid and the rotor. This includes the turbine, which converts fluid energy to mechanical energy, and compressors, which serve the opposite function.
By this definition, it can be inferred that the performance of turbomachinery heavily relies on fluid properties, the geometry of the machine, and operating conditions. The evaluation of these factors is essential for the calculation of the turbomachinery flow coefficient, which is an important parameter for optimizing the design to maximize the efficiency of the turbomachinery.
Turbomachinery Flow Coefficient
The turbomachinery flow coefficient, or flow coefficient, is simply the parameter that indicates the efficiency of the turbomachine, i.e., how well the component can transfer fluid energy to the rotating shaft and vice versa. It is a dimensionless parameter that can be mathematically expressed as:
Ф is the turbomachinery flow coefficient
m is the mass flow rate
ρ is the density of the fluid
A is the area of the flow passage
U is the rotational speed, i.e., U = rotational velocity x radius
However, when we consider a turbomachine with an inlet and outlet system for the fluid, it is important to consider factors like velocity and pressure difference.
The mass flow rate can be calculated as:
The power required for moving the fluid from the inlet to the outlet is:
P = power
η = machine efficiency
∆p = pressure difference = inlet pressure  outlet pressure
Considering a uniform velocity of fluid across the machine, the kinetic energy at the outlet can be calculated as:
The turbomachinery flow coefficient can then be calculated as:
This equation can be further elaborated as:
The above equation is principal in evaluating the performance of turbomachinery such as turbines, compressors, or pumps. The ability to handle large mass flow rates for a given pressure differential indicates high efficiency and viceversa.
Enhancing Efficiency With Turbomachinery Design Optimization
The first step to improving machine efficiency is to understand the factors that affect the turbomachinery flow coefficient.
Machine geometry 
The shape and size of the machine, i.e, the crosssectional area of the flow passage, number of blades, their angles, curvature, etc., can have an impact on the flow rate, flow behavior, and pressure at the outlet. 
Operating condition 
Inlet conditions such as the flow intensity, velocity profile, and distortion can affect the mass flow rate and pressure difference in the turbomachinery. This is also impacted by fluid properties such as density and viscosity. 
Reynolds number 
Whether the flow in the machine is laminar or turbulent can influence the value of the turbomachinery flow coefficient. Usually, at low Reynolds numbers – laminar flow – the flow coefficient is generally higher. Similarly, at a high Reynolds number – turbulent flow – the flow coefficient has lower values. 
With computational fluid dynamics (CFD), the analysis of flow behavior within the turbomachinery can be simplified. CFD simulation facilitates visualization of the flow field and provides detailed insight into parameters like velocity gradient, pressure distribution, flow patterns, etc. The numerical evaluation of these parameters is key to analyzing turbomachine performance and identifying opportunities for design optimization to improve efficiency.
Calculating the Turbomachinery Flow Coefficient With CFD Simulation
For CFD simulation of turbomachinery, the geometry and boundary conditions are first defined, and the fluid flow domain is discretized into a finite number of elements. Here, the NavierStokes equations associated with the fluid motion are solved. The results obtained for parameters like mass flow rate, density, pressure difference, and crosssectional area can then be used to calculate the turbomachinery flow coefficient.
CFD simulation and analysis can be done under different operating conditions to gain insight into how the machine geometries, flow regimes, and fluid properties can influence the flow coefficient and how it can impact the performance of the machine. With tools such as Fidelity and Fidelity Pointwise, engineers can easily perform the simulation and derive the results to make decisions about how the design can be optimized to provide high efficiency with low energy consumption.
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