Low Reynolds Number Turbulent Flow Research Articles

Laminarization of Low Reynolds Number Turbulent Flow in Heated Rotating Pipe

Numerical investigation of laminarization of low Reynolds number turbulent flow in a heated rotating vertical pipe is carried out using a rotation-sensitized k-ω Shear Stress Transport (SST) model with modifications to include low Reynolds number flow effects. The results show that rotation accelerates laminarization in heated pipes and leads to as much as 72% deterioration in heat transfer for a typical inlet Reynolds number of 5000 and at a rotation number of 2. Rotation causes a reduction of the velocity gradients in the near-wall region. The lower gradients result in a reduction in the rate of production of turbulence kinetic energy, which causes the flow to laminarize. A laminarization map that relates the nondimensional heat flux as a function of inlet Reynolds number and rotation number is presented in this study. Correlation to predict the nondimensional wall heat flux required to laminarize the flow as a function of inlet Reynolds number and rotation number is proposed. The proposed laminarization map and the correlation which predicts the nondimensional heat flux required for laminarization to within an accuracy of ±8.1% accuracy for flow of air in a heated rotating vertical pipe would be of value to operators and designers of heat exchangers using air as a working medium to maintain a heat flux or a rotation number below the threshold value to prevent flow laminarization.

Numerical study of transient convective turbulent boundary layer flow along a vertical plate: analysis of kinetic energy and its dissipation rate

ABSTRACT The present article numerically investigates the turbulent buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model. The deployed turbulence model is appropriate for low Reynolds number (LRN) turbulent flow adjacent to a solid boundary, and the turbulence kinetic energy (TKE) and dissipation rate of TKE are estimated using the momentum equations and are solved simultaneously with the mean flow conservation equations. Two-dimensional time-dependent viscous incompressible turbulent flow is simulated. This flow domain is governed by a highly non-linear group of partial differential equations, namely the time-averaged continuity, momentum, and energy, and also the flow property is determined through TKE, and dissipation rate of TKE equations. Since these equations are not solvable using analytical methods, an implicit second-order finite difference method is employed to solve the governing turbulent flow equations numerically. The simulated time-averaged velocity, temperature, TKE, and dissipation rate of TKE profiles along with friction factor and heat transfer rate are computed for different values of turbulent Reynolds and Prandtl numbers. Average velocity, temperature, turbulence energy, and dissipation rate under both transient and steady-state conditions are decreased with increment in . There is a decrement in average transient velocity and turbulence energy rates with increasing values, whereas the average temperature profile increases. Average steady temperature and turbulence energy profiles are also enhanced with rising values of . The majority of researchers focus on laminar flow and thus far turbulent flow has mainly been addressed through experiments only. To better elucidate the flow in this condition, the novelty of the present study is to utilize a numerical FDM procedure to probe more deeply into the turbulence characteristics in buoyancy-driven (natural convection) flow along a vertical plate with a low Reynolds turbulence two-equation k-ϵ model, as this topic is fundamental to many applications in science and engineering. Furthermore, the results of the turbulent flow simulations obtained from the current model are corroborated with existing results for the special case of laminar flow and a good correlation is achieved.

KεNet: discovering the turbulence model and applying for low Reynolds number turbulent channel flow

kεNet: discovering the turbulence model and applying for low Reynolds number turbulent channel flow

A Numerical Investigation of an Artificially Roughened Solar Air Heater

Solar air heating devices have been employed in a wide range of industrial and home applications for solar energy conversion and recovery. It is a useful technique for increasing the rate of heat transfer by artificially creating repetitive roughness on the absorbing surface in the form of semicircular ribs. A thermo-hydraulic performance analysis for a fully developed turbulent flow through rib-roughened solar air heater (SAH) is presented in this article by employing computational fluid dynamics. Both 2-dimensional geometrical modeling and numerical solutions were performed in the finite volume package ANSYS FLUENT. The renormalization-group (RNG) k-ε turbulence model was used, as it is suitable for low Reynolds number (Re) turbulent flows. A thermo-hydraulic performance analysis of an SAH was carried out for a ranging Re, 3800–18,000 (6 sets); relative roughness pitch (RRP), 5–25 (12 sets); relative roughness height (RRH), 0.03–0.06 (3 sets); and heat flux, 1000 W/m2. The numerical analysis revealed that with an RRP of 5 and an RRH of 0.06, the roughened duct produces the highest augmentation in average Nur in the order of 2.76 times that of a plain duct at an Re of 18,000. With an RRP = 10 and RRH = 0.06, the roughened duct was found to provide the most optimum thermo-hydraulic performance parameter (THPP). The THPP was determined to have a maximum value of 1.98 when the Re is equal to 15,000. It was found that semi-circular ribs which have a rib pitch = 20 mm and a rib height = 2 mm can be applied in an SAH to enhance heat transfer.

온도차와 플랩 위치가 이중 구조 익형의 성능에 주는 영향에 대한 수치적 연구

The significance of low Reynolds flows increased due to the emergence of low speed flying vehicles. Therefore, the flow control methods deserve more attention. In the present study, the application of a differential temperature on the surfaces of a slotted double-element airfoil is numerically evaluated at a low Reynolds number turbulent flow condition. The main objective is to study the effects of differential temperature on the aerodynamics of the airfoil at various flap positions. Six flap positions were considered utilizing the overset meshing techniques after appropriate parameterization of the flap locations. The numerical results were validated against previous experimental results, and subsequently, the effects of the differential temperature on the aerodynamics of baseline and other configurations were clearly explained. The best configurations were identified with and without the presence of differential temperature. Moreover, it was found out that among all the considered configurations, a maximum of 4% increase in lift and 5% reduction in drag can be achieved through the application.

Turbulent Skin Friction Reduction through the Application of Superhydrophobic Coatings to a Towed Submerged SUBOFF Body

Abstract In the present study, the drag-reducing effect of sprayed superhydrophobic surfaces (SHSs) is determined for two external turbulent boundary layer (TBL) flows. We infer the modification of skin friction created beneath TBLs using near-wall laser Doppler velocity measurements for a series of tailored SHSs. Measurements of the near-wall Reynolds stresses were used to infer reduction in skin friction between 8%and 36%in the channel flow. The best candidate SHS was then selected for application on a towed submersible body with a SUBOFF profile. The SHS was applied to roughly 60% of the model surface over the parallel midbody of the model. The measurements of the towed resistance showed an average decrease in the overall resistance from 2% to 12% depending on the speed and depth of the towed model, which suggests a SHS friction drag reduction of 4–24% with the application of the SHS on the model. The towed model results are consistent with the expected drag reduction inferred from the measurements of a near-zero pressure gradient TBL channel flow. Introduction Nature has provided a plethora of materials to be studied and mimicked for everyday applications (Jung & Bhushan 2010). One material pertinent for use in the marine environment is the lotus leaf, which is known for its self-cleansing properties and resistance to wetting (Neinhuis & Barthlott 1997). More specifically, lotus-inspired superhydrophobic surfaces (SHSs) have been biomimetically developed for skin friction reduction in various flow applications (Bhushan et al. 2009; Samaha et al. 2012). Being exhaustively studied in small-scale laminar flows (see Rothstein [2010] for a review of SHS drag reduction and slip on SHSs), advances in the design and fabrication of SHSs have permitted application of these materials in more naval-relevant flows. Previously, it has been shown that in laminar flow, SHSs can reduce drag (Watanabe et al. 1999; Ou et al. 2004; Ou & Rothstein 2005; Zhao et al. 2007; Daniello et al. 2009; Woolford et al. 2009), and in low–Reynolds number turbulent flows, SHS drag reduction has been observed using small-scale, structured surfaces and large air–water interfaces (Henoch et al. 2006; Daniello et al. 2009; Park et al. 2014). However, these surfaces, in higher turbulence flows, can be unstable or become wetted. If the SHS possesses roughness features with small scales compared with the viscous length scale of the flow, researchers have demonstrated SHS friction drag reduction for wall-bounded, high–Reynolds number turbulent flows (Zhao et al. 2007; Aljallis et al. 2013; Bidkar et al. 2014; Golovin et al. 2016; Ling et al. 2016b; Gose et al. 2018a).

Laminarization of turbulent flow in a heated vertical finned tube

Laminarization of the turbulent flow of Helium in a heated vertical finned tube was studied using a low-Reynolds number turbulence model. The study was carried out for an inlet Reynolds number of 6000, a non-dimensional wall heat flux value of 0.003, the number of fins ranging from 8 to 24, and non-dimensional fin height ranging from 0.1 to 0.3. Reductions in turbulent kinetic energy production and low-velocity regions in the inter-fin region are observed which promoted laminarization. Also, for low Reynolds number turbulent flow with large heat fluxes, the finned tubes are found to offer comparatively lower heat transfer enhancement at the expense of a larger pressure drop penalty.

Active control for drag reduction of turbulent channel flow based on convolutional neural networks

An active controller based on convolutional neural networks (CNNs) is designed for drag reduction of turbulent channel flow. CNNs are constructed to predict the normal velocities on the detection plane as wall blowing and suction using measurable quantities at the wall, i.e., spanwise or streamwise wall shear stress. The training data of CNNs are generated from the direct numerical simulation of channel flow. With different wall quantities, we design and train different CNNs for flow prediction. The purpose is to identify which wall quantity is associated with substantial drag reduction. A linear neural network based on the spanwise wall shear stress shows sufficient capability to predict the inflow field and obtain almost the same drag reduction rate as the opposite control, which does not perform well when using the streamwise wall shear stress as the input. Hence, a nonlinear CNN model with activation function and multiple convolutional layers is established to use the streamwise wall shear stress for flow prediction and drag reduction control. Applying the trained CNNs to a low Reynolds number turbulent channel flow at Reτ = 100, we obtain up to 19% and 10% drag reduction rates based on the spanwise and streamwise wall-shear stresses, respectively. These networks are also tested at different Reynolds numbers, i.e., Reτ = 180 and Reτ = 390, where substantial drag reduction rates are obtained as well. Effects of the controller on turbulent instantaneous flow field and statistics are presented.

On the origin of drag increase in varying-phase opposition control

This study investigates the physics underlying the drag increase in a low Reynolds number turbulent channel flow due to varying-phase opposition control by means of direct numerical simulation and modal analysis. The drag increase occurs for an extended region of the parameter space and we consider a controller with a positive phase shift in Fourier domain between sensor measurement and actuator response as a representative example for this regime. Analyses of instantaneous flow fields as well as spatial power spectra show that the structure of drag-increased flows is remarkably different from that of drag-reduced and canonical flows. In particular, the near-wall region is dominated by structures of short streamwise and large spanwise extent. Isolation of a representative control scale shows that these energetic structures can be characterized as spanwise rollers, which induce strong ejection and sweep motions and lead to drag increase. The presence of rollers, and therefore drag increase, in the full nonlinear system correlates well with the presence of an amplified eigenvalue in the eigenspectrum of the linearized Navier–Stokes operator. It is further shown that the scales responsible for drag increase at positive phase shifts are inactive at negative phase shifts and do not contribute to drag reduction. These scales can therefore be excluded from a controller aimed at drag reduction, which relaxes the spatial resolution requirements on the control hardware. The eigenspectrum may be used as a computationally cheap tool to identify such detrimental scales during an early design stage.

Low Reynolds number turbulent flows over elastic walls

We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, in turn, amplify the turbulent Reynolds stresses in the fluid. At a very low Reynolds number, the only production term is due to the energy input from the elastic wall, which increases with the wall elasticity. This mechanism may be exploited to passively enhance mixing in microfluidic devices.

Mathematical foundation of turbulence generation—From symmetric to asymmetric Liutex

Vortices have been regarded as the building blocks and muscles of turbulence for a long time. To better describe and analyze vortices or vortical structures, recently a new physical quantity called Liutex (previously named Rortex) is introduced to present the rigid rotation part of fluid motion (Liu et al. 2018). Since turbulence is closely related to the vortex, it can be postulated that there exists no turbulence without Liutex. According to direct numerical simulations (DNS) and experiments, forest of hairpin vortices has been found in transitional and low Reynolds number turbulent flows, while one-leg vortices are predominant in full developed turbulent flows. This paper demonstrates that the hairpin vortex is unstable. The hairpin vortex will be weakened or lose one leg by the shear and Liutex interaction, based on the Liutex definition and mathematical analysis without any physical assumptions. The asymmetry of the vortex is caused by the interaction of symmetric shear and symmetric Liutex since the smaller element of a pair of vorticity elements determines the rotational strength. For a 2-D fluid rotation, if a disturbance shear effects the larger element, the rotation strength will not be changed, but if the disturbance shear effects the smaller element, the rotation strength will be immediately changed due to the definition of the Liutex strength. For a rigid rotation, if the shearing part of the vorticity and Liutex present the same directions, e.g., clockwise, the Liutex strength will not be changed. If the shearing part of the vorticity and Liutex present different directions, e.g., one clockwise and another counterclockwise, the Liutex strength will be weakened. Consequently, the hairpin vortex could lose the symmetry and even deform to a one-leg vortex. The one-leg vortex cannot keep balance, and the chaotic motion and flow fluctuation are doomed. This is considered as the mathematical foundation of turbulence formation. The DNS results of boundary layer transition are used to justify this theory.

WATER HAMMER IN PIPELINE WITH DIFFERENT CHARACTERISTICS OF VALVE CLOSING AND UNSTEADY WALL FRICTION

This paper presents an analytical investigation of water hammer pressure variation in a reservoir-pipe-valve system. Laplace transform method is used to get the analytical solutions for different characteristics of the valve closing. Specifically, sudden valve closing and piecewise linear closing are used, the latter can be treated as approximated arbitrary characteristics of valve closing. Unsteady wall friction is also included. The new solutions compare well with the previous experimental data. The results show that this solution is suitable for water hammer with laminar and low Reynolds number turbulent unsteady flow. The effects of different characteristics of the valve closing on the water hammer pressure variations are also studied. This solution can be a better choice for optimization of valve closing to reduce the maximum water hammer pressure.

A Control Forced Concurrent Precursor Method for LES Inflow

With the increased application of large eddy simulation techniques, the generation of realistic turbulence at inflow boundaries is crucial for the accuracy of a simulation. The Control Forced Concurrent Precursor Method (CFCPM) proposed in this work combines an existing concurrent precursor method and a mean flow forcing method with a new extension of the controlled forcing method to impose turbulent inflow boundary conditions primarily, although not exclusively, for domains that require periodic boundary conditions. Turbulent inflow boundary conditions are imposed through a region of body forces added to the momentum equations of the main simulation that transfers the precursor simulation into the main domain. Controlled forcing planes, which come into play as body forces added to the momentum equations on planes perpendicular to the flow, located in the precursor simulation, allow for specific Reynolds stress tensors and mean velocities to be imposed. The mean flow controlled forcing method only modifies the mean velocity profiles, leaving the fluctuating velocity field untouched. The proposed fluctuating flow controlled forcing methods extends the application of the original controlled forcing method to multiple fluctuating velocity components and couples their calculation in order to amplify the existing fluctuations present in the precursor flow field so that prescribed anisotropic Reynolds stress tensors can be reproduced. The new method was tested on high Reynolds number turbulent boundary layer flow over a wall-mounted cube and low Reynolds number turbulent boundary layer flow over a backward-facing step. It was found that the new extension of the controlled forcing method reduced the development time for both test cases considered here when compared to not using controlled forcing and only using the original controlled forcing method.

Direct numerical simulation of polydisperse aerosol particles deposition in low Reynolds number turbulent flow

Aerosol behaviors have a great effect on the evaluation of the leak rate of the coolant in the concept of Leak Before Break (LBB) in the Nuclear Power Plant (NPP) as the coolant will be released into the containment mainly in the form of aerosols if there exists a leak in the primary loop. The transportation and deposition of aerosol particles strongly affect the accuracy of evaluating the leakage source term. In this paper, direct numerical simulation coupled with Lagrangian particle tracking is proposed aiming at the transportation and deposition of polydisperse micron-sized particles in low Reynolds number turbulent horizontal flow. Results are validated by several theoretical and empirical equations. The study reveals the diffusion and deposition mechanism of particles with different sizes. It indicates that gravity plays a main role in the deposition of large particles (dp > 10 μm) in the low Reynolds number turbulent flow (Re < 6000). For small particles, deposition is mainly determined by the turbulence and Brownian motion. The size distribution of the deposited particles is different with the initial particle size distribution, which indicates that the particle size distribution in the containment may be not the same as the leaked particle size distribution.

Non-normality and classification of amplification mechanisms in stability and resolvent analysis

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how non-normality from mean shear distributes perturbation energy in different velocity components of the forcing and response modes. The inverse of their inner product, which is unity for a purely normal mechanism, is proposed as a measure to quantify non-normality. In flows where there is downstream spatial dependence of the base/mean, mean flow advection separates the spatial support of forcing and response modes which impacts the inner product. Success of mean stability analysis depends on the normality of amplification. If the amplification is normal, the resolvent operator written in its dyadic representation reveals that the adjoint and forward stability modes are proportional to the forcing and response resolvent modes. If the amplification is non-normal, then resolvent analysis is required to understand the origin of observed flow structures. Eigenspectra and pseudospectra are used to characterize these phenomena. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The first deals mainly with normal mechanisms and quantification of non-normality using the inverse inner product of the leading forcing and response modes agrees well with the product of the resolvent norm and distance between the imaginary axis and least stable eigenvalue. In turbulent channel flow, structures result from both normal and non-normal mechanisms. Mean shear is exploited most efficiently by stationary disturbances while bounds on the pseudospectra illustrate how non-normality is responsible for the most amplified disturbances at spatial wavenumbers and temporal frequencies corresponding to well-known turbulent structures.

Clustering of Inertial Particles in Turbulent Channel Flow

Particle clustering phenomenon is relevant to many industrial and natural systems. Particles denser than the carrier fluid tend to accumulate in the high-strain low-vorticity regions, which leads to inhomogeneous distribution of particles. This phenomenon is known as “preferential concentration”. The deposition and entrainment of particles in low-Reynolds number turbulent channel flow is well understood. However, particles clustering under the influence of multi-scale vortices in high-Reynolds-number turbulent channel flow is not fully investigated. Present study aims to understand this situation through the DNS of particle-laden turbulent channel flow at Reτ = 500 and 1000.

CFD and 1D Approaches for the Unsteady Friction Analysis of Low Reynolds Number Turbulent Flows

AbstractThe aim of this paper is to investigate the complex nature of the transient energy dissipation by using a computational fluid dynamics (CFD) model with a high spatial and temporal resolutio...

The dissipation tensor in wall turbulence

The paper investigates the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$in wall turbulence. Available direct numerical simulation (DNS) data are examined to illustrate the differences in the anisotropy of the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$with respect to the anisotropy of the Reynolds stresses$\unicode[STIX]{x1D633}_{ij}$. The budgets of the transport equations of the dissipation tensor$\unicode[STIX]{x1D700}_{ij}$are studied using novel DNS data of low Reynolds number turbulent plane channel flow with spatial resolution sufficiently fine to accurately determine the correlations of products of two-derivatives of fluctuating velocities$u_{i}^{\prime }$and pressure$p^{\prime }$which appear in various terms. Finally, the influence of the Reynolds number on the diagonal components of$\unicode[STIX]{x1D700}_{ij}$($\unicode[STIX]{x1D700}_{xx}$,$\unicode[STIX]{x1D700}_{yy}$,$\unicode[STIX]{x1D700}_{zz}$) and on the various terms in their transport equations is studied using available DNS data of Vreman and Kuerten (Phys. Fluids, vol. 26, 2014b, 085103).

Laminar-to-turbulence and relaminarization zones detection by simulation of low Reynolds number turbulent blood flowinlarge stenosed arteries.

Laminar, turbulent, transitional, or combine areas of all three types of viscous flow can occur downstream of a stenosis depending upon the Reynolds number and constriction shape parameter. Neither laminar flow solver nor turbulent models for instance the k-ω (k-omega), k-ε (k-epsilon), RANS or LES are opportune for this type of flow. In the present study attention has been focused vigorously on the effect of the constriction in the flow field with a unique way. It means that the laminar solver was employed from entry up to the beginning of the turbulent shear flow. The turbulent model (k-ω SST Transitional Flows) was utilized from starting of turbulence to relaminarization zone while the laminar model was applied again with onset of the relaminarization district. Stenotic flows, with 50 and 75% cross-sectional area, were simulated at Reynolds numbers range from 500 to 2000 employing FLUENT (v6.3.17). The flow was considered to be steady, axisymmetric, and incompressible. Achieving results were reported as axial velocity, disturbance velocity, wall shear stress and the outcomes were compared with previously experimental and CFD computations. The analogy of axial velocity profiles shows that they are in acceptable compliance with the empirical data. As well as disturbance velocity and wall shear stresses anticipated by this new approach, part by part simulation, are reasonably valid with the acceptable experimental studies.

Numerical study of turbulent flow in asymmetrically heated horizontal channel

Low Reynolds number turbulent flow of Helium in a horizontal channel subjected to asymmetric heating was studied using a low-Reynolds number turbulence model. The study was conducted for inlet Reynolds number ranging from 4000 to 10,000, non-dimensional wall heat flux ranging from 0.001 to 0.005, and ratio of top wall heat flux to bottom wall heat flux ranging from 0 to 1. The results from the study were used to obtain laminarization criterion as a function of inlet Reynolds number, non-dimensional wall heat flux, and ratio of top wall heat flux to bottom wall heat flux. The developed laminarization criteria which is based on the ratio of turbulence production to turbulence dissipation predicts a reduction in the Nusselt number as compared to the constant property turbulent flow results, ranging from as much as 45% reduction for inlet Reynolds number of 4000 to 22% reduction for inlet Reynolds number of 10,000.