Non-linear low-Reynolds Number Research Articles

End-to-end efficiency quantification of an autonomous underwater vehicle propulsion system

Increasing demand for versatile and long-endurance autonomous underwater vehicles puts significant design pressure on all aspects of AUV design and operation, including that of the propulsive system. The present study discusses testing of a thruster unit and several propellers developed to propel a hybrid glider/flight-style underwater vehicle. Due to the AUV being required to operate at largely different speeds and thrust levels between the two configurations, the propulsive subsystem needs to be capable of remaining efficient and effective across a wide range of operating conditions. Thus, the current results focus on quantifying all of the factors affecting the drive train, ranging from open-water performance of the propeller up to electro-mechanical efficiency of the magnetic coupling and geared electric motor. It is shown that, depending on the required operating point, total efficiency of the vehicle is primarily affected by non-linear low Reynolds number effects, sudden drop of gearbox efficiency at low revolutions and applied torques, as well as blade deformation, aside of the baseline propeller efficiency.

Application of linear and non-linear low- Re k– ε models in two-dimensional predictions of convective heat transfer in passages with sudden contractions

This paper presents comparisons between heat transfer predictions and measurements for developing turbulent flow through straight rectangular channels with sudden contractions at the mid-channel section. The present numerical results were obtained using a two-dimensional finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the well-known SIMPLE algorithm. The hybrid scheme was employed for the discretization of convection in all transport equations. For modeling of the turbulence, a zonal low-Reynolds number k– ε model and the linear and non-linear low-Reynolds number k– ε models with the “Yap” and “NYP” length-scale correction terms have been employed. The main objective of present study is to examine the ability of the above turbulence models in the prediction of convective heat transfer in channels with sudden contraction at a mid-channel section. The results of this study show that a sudden contraction creates a relatively small recirculation bubble immediately downstream of the channel contraction. This separation bubble influences the distribution of local heat transfer coefficient and increases the heat transfer levels by a factor of three. Computational results indicate that all the turbulence models employed produce similar flow fields. The zonal k– ε model produces the wrong Nusselt number distribution by underpredicting heat transfer levels in the recirculation bubble and overpredicting them in the developing region. The linear low- Re k– ε model, on the other hand, returns the correct Nusselt number distribution in the recirculation region, although it somewhat overpredicts heat transfer levels in the developing region downstream of the separation bubble. The replacement of the “Yap” term with the “NYP” term in the linear low- Re k– ε model results in a more accurate local Nusselt number distribution. Moreover, the application of the non-linear k– ε model further improves the thermal predictions. In general, among the three turbulence models examined, the non-linear low- Re k– ε model produces the best heat transfer predictions.

Turbulent flow and heat transfer in a square-sectioned U-bend

Turbulent flow and heat transfer in a square-sectioned U-bend are investigated. Turbulence models with linear and non-linear expressions for the Reynolds stresses are used. The near wall turbulence is treated by the damping functions approach and a two-layer model with Wolfshtein's sub-layer treatment. The inlet conditions have a significant effect on the predictions. The results from the non-linear low-Reynolds number k-ε models including Suga's cubic low-Re model were closest to experimental data. These models predicted the stress-induced secondary motion in the straight inlet duct well. This secondary motion had a small impact on the flow in the bend.

Numerical simulation of wake velocity and wake turbulence effects on unsteady boundary layer transition

Linear and non-linear low Reynolds number k-ɛ eddy viscosity models are applied to the simulation of unsteady transitional flows pertinent to axial turbomachine aerodynamics. Adequate test cases are selected to allow an individual investigation of wake velocity and wake turbulence effects on unsteady transition induced by separation bubbles and wake passing respectively. Separation bubbles under steady main flow conditions are calculated first, demonstrating the applicability of the numerical scheme and the selected turbulence models. Unsteady simulations show that essential features of the experimental investigation can be reproduced, although oscillation characteristics of the separation bubble, such as phase shifts, can only be partly reproduced. Predictions of wake-induced transition on a flat plate agree with the underlying direct numerical simulation study in many important aspects. However, simulation results show deficiencies with respect to the time-averaged transition length and the spatio-temporal evolution of turbulent flow regions.

Application of non-linear k -ω model to a turbulent flow inside a sharp U-bend

Simulation of the complex flow inside a sharp U-bend needs both refined turbulence models and higher order numerical discretization schemes. In the present study, a non-linear low-Reynolds number (low-Re) k–ω model including the cubic terms was employed to predict the turbulent flow through a square cross-sectioned U-bend with a sharp curvature, R C/D = 0.65. In the turbulence model employed for the present study, the cubic terms are incorporated to represent the effect of extra strain-rates such as streamline curvature and three-dimensionality on both turbulence normal and shear stresses. In order to accurately predict such complex flowfields, a higher-order bounded interpolation scheme (Song et al., 1999) has been used to discretize all the transport equations. The calculated results by using both the non-linear k–ω model and the linear low-Reynolds number k–ɛ model (Launder and Sharma, 1974) have been compared with experimental data. It is shown that the present model produces satisfactory predictions of the flow development inside the sharp U-bend and well captures the characteristics of the turbulence anisotropy within the duct core region and wall sub-layer.

A nonlinear low-Reynolds number heat transfer model for turbulent separated and reattaching flows

A nonlinear low-Reynolds number heat transfer model is developed to predict turbulent flow and heat transfer in separated and reattaching flows. The k– ε– f μ model of Park and Sung (T.S. Park, H.J. Sung, A new low-Reynolds-number model for predictions involving multiple surface, Fluid Dynamics Research 20 (1997) 97–113) is extended to a nonlinear formulation, based on the nonlinear model of Gatski and Speziale (G.B. Gatski, C.G. Speziale, On explicit algebraic stress models for complex turbulent flows, J. Fluid Mech. 254 (1993) 59–78). The limiting near-wall behavior is resolved by solving the f μ elliptic relaxation equation. An improved explicit algebraic heat transfer model is proposed, which is achieved by applying a matrix inversion. The scalar heat fluxes are not aligned with the mean temperature gradients in separated and reattaching flows; a full diffusivity tensor model is required. The near-wall asymptotic behavior is incorporated into the f λ function in conjunction with the f μ elliptic relaxation equation. Predictions of the present model are cross-checked with existing measurements and DNS data. The model performance is shown to be satisfactory.

A Non-linear Low-Reynolds-Number Heat Transfer Model for Turbulent Separated and Reattaching Flows

A nonlinear low-Reynolds number heat transfer model is developed to predict turbulent flow and heat transfer in separated and reattaching flows. The k‐e‐fm model of Park and Sung (T.S. Park, H.J. Sung, A new low-Reynoldsnumber model for predictions involving multiple surface, Fluid Dynamics Research 20 (1997) 97‐113) is extended to a nonlinear formulation, based on the nonlinear model of Gatski and Speziale (G.B. Gatski, C.G. Speziale, On explicit algebraic stress models for complex turbulent flows, J. Fluid Mech. 254 (1993) 59‐78). The limiting nearwall behavior is resolved by solving the fm elliptic relaxation equation. An improved explicit algebraic heat transfer model is proposed, which is achieved by applying a matrix inversion. The scalar heat fluxes are not aligned with the mean temperature gradients in separated and reattaching flows; a full diAusivity tensor model is required. The nearwall asymptotic behavior is incorporated into the fl function in conjunction with the fm elliptic relaxation equation. Predictions of the present model are cross-checked with existing measurements and DNS data. The model performance is shown to be satisfactory. # 2000 Elsevier Science Ltd. All rights reserved.

Numerical prediction of heat and momentum transfer over micro-grooved surface with a nonlinear k– ε model

The paper reports numerical results obtained in a fully developed turbulent channel flow with triangular riblets. The heat and momentum transfer characteristics are calculated by using a nonlinear low-Reynolds number k– ε model together with several turbulent scalar flux representations. Comparison of the drag variation prediction with previous experimental and numerical data shows that the present turbulence model can simulate the turbulent flow over this complex surface reasonably well. By comparing the results obtained with the isotropic and anisotropic Reynolds stress representations, the significance of the mean secondary flow in the drag reduction mechanism is discussed. In both drag reducing and increasing conditions, the drag change predicted is found to be in close agreement with the data available in the literature. Under the drag reducing conditions, possible departure from the Reynolds analogy is investigated at various Reynolds and Prandtl numbers. It is shown that, while the skin friction is reduced over the riblet surface, the heat transfer performance can actually be increased beyond that on a smooth wall, although discrepancy with the experimental data is not negligible.