Derivation of Navier–Stokes equation in rotational frame for engineering flow analysis

Menon, Sananth H.; A, Ramachandra Rao; Mathew, Jojo; Jayaprakash, J.

doi:10.1016/j.ijft.2021.100096

Cited by 7 publications

(4 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Table 2 illustrates the investigation of the three moments in the CFD simulation cases, leading to the situations described in the aforesaid definitions. The mathematical expression of the idle and thrust moments with aspect to ω and U 1 is derived from the steady state and incompressible flow modified Navier-Stokes equations in the MRF form, containing the additional centrifugal force terms in the momentum conservation shown as Equation ( 12) [34]. The source term of the relative coordinate system is used to derive the expression of idle moment M Idle on the rotor plate through integration as Equation (13).…”

Section: Moment Analysis Methodsmentioning

confidence: 99%

The Biffis Canal Hydrodynamic System Performance Study of Drag-Dominant Tidal Turbine Using Moment Balancing Method

Zhang,

Ng,

Mittal

2023

Sustainability

View full text Add to dashboard Cite

Drag-dominant tidal turbine energy holds tremendous clean energy potential but faces significant hurdles as unsuitability of the actuator disc model due to the varying swept blockage area, unaccounted bypass flow downstream interaction, and rotor parasitic drag, whereas blade element momentum theory is computably effective for majorly 3-blade lift-dominated aerofoil. This study validates a novel method to find the optimal TSR of any turbine with a cost-effective and user-friendly moment balancing algorithm to support robust tidal energy development. Performance analysis CFD study of Pinwheel and Savonius tidal turbines in a Biffis canal hydrodynamic system was carried out. Thrust and idle moment are analyzed as functions of only inlet fluid velocity and rotational speed, respectively. These relationships were verified through regression analysis, and the turbines’ net moment equations were established based on these parameters. In both simulation models, rotational speed and inlet velocity were proved excellent predictor variables (R2 value ≈ 1) for idle and thrust moments, respectively. The optimal TSR values for Pinwheel and Savonius turbines were 2.537 and 0.671, respectively, within an acceptable error range for experimental validation. The optimal basin efficiency (ηopt, TSR) values for Pinwheel and Savonius in the 12% blockage channel were (29.09%, 4.0) and (25.67%, 2.87), respectively. The trade-off between TSRopt and ηopt is the key instruction concerning electricity generation and environmental impact.

show abstract

Section: Moment Analysis Methodsmentioning

confidence: 99%

The Biffis Canal Hydrodynamic System Performance Study of Drag-Dominant Tidal Turbine Using Moment Balancing Method

Zhang,

Ng,

Mittal

2023

Sustainability

View full text Add to dashboard Cite

show abstract

“…The RANS mean mass and momentum transport equations in the moving rotational frame (MRF) system were written as Equations ( 13) and ( 14) in integral form. The steadystate and incompressible flow during the idle moment is governed by the modified Navier-Stokes equations in the MRF [38]. These equations include additional centrifugal force terms in the momentum conservation, resulting in the derivation of Equation ( 14) as Equation (15).…”

Section: Thrust and Idle Moment Equationmentioning

confidence: 99%

CFD Validation of Moment Balancing Method on Drag-Dominant Tidal Turbines (DDTTs)

Zhang

Mittal

2023

Processes

View full text Add to dashboard Cite

Current performance analysis processes for drag-dominant tidal turbines are unsuitable as disk actuator theory lacks support for varying swept blockage area, bypass flow downstream interaction, and parasitic rotor drag, whereas blade element momentum theory is computably effective for three-blade lift-dominated aerofoil. This study proposes a novel technique to calculate the optimal turbine tip speed ratio (TSR) with a cost-effective and user-friendly moment balancing algorithm. A reliable dynamic TSR matrix was developed with varying rotational speeds and fluid velocities, unlike previous works simulated at a fixed fluid velocity. Thrust and idle moments are introduced as functions of inlet fluid velocity and rotational speed, respectively. The quadratic relationships are verified through regression analysis, and net moment equations are established. Rotational speed was a reliable predictor for Pinwheel’s idle moment, while inlet velocity was a reliable predictor for thrust moment for both models. The optimal (Cp, TSR) values for Pinwheel and Savonius turbines were (0.223, 2.37) and (0.63, 0.29), respectively, within an acceptable error range for experimental validation. This study aims to improve prevailing industry practices by enhancing an engineer’s understanding of optimal blade design by adjusting the rotor speed to suit the inlet flow case compared to ‘trial and error’ with cost-intensive simulations.

show abstract

“…The two varying independent variables i.e., 𝑈 1 and 𝜔 comprise a dynamic Tip Speed Ratio (TSR) matrix using Eq. (10), shown for both turbines as Table 2a,b. The turbine's optimal TSR can be obtained by the Cp -TSR curve.…”

Section: Moment Analysismentioning

confidence: 99%

Parametric Optimization Analysis of Pinwheel and Savonius Drag-Dominant Tidal Turbines Performance with Moment Balancing Method

Zhang,

Ng,

Shivansh

2023

Preprint

View full text Add to dashboard Cite

Drag-dominant tidal turbine energy holds tremendous clean energy potential but faces significant hurdles as unsuitability of Disk Actuator theory due to the varying swept blockage area, unaccounted bypass flow downstream interaction and rotor parasitic drag whereas Blade Element Momentum theory is computably effective for majorly 3-blade lift-dominated aerofoil. This study proposes a novel method to find the optimal TSR of any turbine with a cost-effective and user-friendly Moment Balancing algorithm to support robust tidal energy development. Performance analysis CFD study of Pinwheel and Savonius tidal turbines was carried out. Dynamic TSR matrix was developed with varying rotational speeds and fluid velocities for reliability, unlike previous works simulated at a fixed fluid velocity. Novel parameters such as thrust and idle moment are introduced as functions of only inlet fluid velocity and rotational speed respectively. These relationships are verified through regression analysis, and the turbines' net moment equations are established based on these parameters. Rotational speed was a reliable predictor for Pinwheel's idle moment, while inlet velocity was a reliable predictor for thrust moment in both models. The optimal (Cp, TSR) values for Pinwheel and Savonius turbines were (2.37, 0.223) and (0.63, 0.16) respectively, within an acceptable error range for experimental validation.

show abstract

Derivation of Navier–Stokes equation in rotational frame for engineering flow analysis

Cited by 7 publications

References 1 publication

The Biffis Canal Hydrodynamic System Performance Study of Drag-Dominant Tidal Turbine Using Moment Balancing Method

The Biffis Canal Hydrodynamic System Performance Study of Drag-Dominant Tidal Turbine Using Moment Balancing Method

CFD Validation of Moment Balancing Method on Drag-Dominant Tidal Turbines (DDTTs)

Parametric Optimization Analysis of Pinwheel and Savonius Drag-Dominant Tidal Turbines Performance with Moment Balancing Method

Contact Info

Product

Resources

About