# Torque and Rotational Speed

### Key Takeaways

Torque is the force producing a rotational motion while rotational speed is the rate of rotation due to that force.

The fluid behavior around the rotational device can be simulated to calculate the torque and rotational speed, which can be used to optimize the design of the turbomachinery.

CFD tools can simulate the complex designs of rotating objects and facilitate the turbulence modeling required for accurate optimization decisions.

*Simulating a centrifugal compressor*

Consider a wind or steam turbine used in the generation of electricity. When the fluid flows over the turbine blades, a rotary force is produced. The magnitude of this force and the speed at which it rotates influences the decision on the shape and size of the blades and the angle of contact with the fluid. These factors affecting the twisting motion are torque and rotational motion.

The analysis of these forces acts as the determinant factor for the performance efficiency of turbines or other turbomachinery. This analysis can be facilitated through the simulation of the behavior of fluids around rotational objects and the calculation of torque and rotational speed using CFD tools.

In this article, we will discuss how engineers can make use of CFD tools to optimize rotational objects through numerical analysis and simulation of flow and associated torque and rotational speed.

## Torque and Rotational Speed in Fluid Dynamics

To understand the effect of fluid motion on the performance of rotating machinery, let us start by defining torque and rotational speed.

Torque is the measure of force that is capable of producing a rotational motion when applied to an object. In a turbine, this force is applied to the shaft when the fluid applies pressure on the blade. Mathematically, torque can be calculated using the following formula:

*Torque formula*

τ is the torque, r is the position vector, i.e., the axis of rotation with respect to the point where force is applied, and F is the applied force, i.e., the position vector.

Rotational speed, on the other hand, is the measure of how fast the object is rotating around an axis after the application of the force. In a turbine, the rotating speed is the rate at which the shaft rotates once the torque is applied. Mathematically, the rotational speed, or angular velocity, can be represented as:

*Rotational speed formula*

ω is the rotational speed or angular velocity, Δፀ is the angular displacement, and Δt is the time taken for the change to occur.

The formula can also be written as:

Alt. rotational speed formula

Here, f is the frequency of rotation.

### Relation Between Torque and Rotational Speed

Torque and rotational speed are interdependent, as the torque identifies the magnitude of the twisting force while rotational speed represents the speed of the rotation due to this force. The relation between the two can be expressed using the power equation:

Power equation

This equation explains the power generated in the turbine with given torque and rotational speed.

## CFD Analysis for Rotational Equipment Design

CFD analysis is crucial in the study of fluid flow and its influences on the dynamics of the rotating system. Through simulation and analysis of fluid flow to the defined shape and size of the rotating blades, engineers can determine whether it can produce the required torque in the shaft. This torque is then transmitted (to the shaft or impeller of the rotor) to calculate the desired rotational speed.

The following are the integral steps in the process.

| - Create a 3D model of the rotating object, such as the turbine that accurately defines its shape and dimension. - Generate a mesh and divide into finite smaller cells. This should be fine enough to capture turbulences in the fluid flow. - The model should accurately represent the flow behavior and rotation of the object. |

| - Define boundary conditions at the inlet and outlet of the flow system. - Specify the velocity and pressure at the inlet and outlet, density and viscosity of the fluid, and rotational speed of the object. |

| -Specify the algorithm to solve the governing equations associated with fluid flow. - Run the simulation and analyze the torque and rotational speed for the design. |

| - Optimize the design of the turbomachinery (impeller, shaft, blades) to achieve the desired torque and rotational speed. - The final design output should provide optimal efficiency and performance. |

## Maximize Rotational Efficiency Through CFD Simulation

Through CFD simulation of the fluid flow and its behavior around rotating objects, engineers and system designers can adjust the shape and size of the blades, the angle at which the fluid comes in contact, and the flow rate to maximize the torque output.

CFD tools such as Cadence’s Fidelity and Fidelity Pointwise can accurately capture the most complex geometries and simulate turbulent flow behavior and unsteady flow conditions. The numerical computation of torque and rotational speed sets the ground for the necessary optimization required in the design of this turbomachinery, so they can be highly efficient with improved performance.

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