Normal Flat Plate Research Articles

Two independent mechanisms with distinct laws for the generation of drag force on accelerating plates

Acceleration of objects in fluids widely exists in biological propulsions and contains rich unsteady fluid mechanisms. In this paper, the instantaneous drag force on accelerating normal flat plates (circular, elliptical, square, and rectangular plates) in a wide range of dimensionless acceleration (a*=16∼2) is measured, and the underlying mechanism for force generation is investigated. At first, we find that the drag force coefficient generally scales with the square root of a* when a*<1.0, coinciding with the scaling law given by Reijtenbagh et al. (PRL. 2023,130,174001). However, the drag force coefficient more linearly scales with a* rather than a* when a*>1.0, thereby indicating acceleration plays two distinct roles on the force generation depending on a*. Moreover, two scaling laws are built to quantitatively describe the two distinct roles of a* on the drag force generation. Based on fluid impulse, the drag force is largely contributed by the added mass of the accelerating plates (added mass force) and vorticity generation fed by the shear layer on the edge of the plates (vortex creation force). When a*<1.0, the vortex creation force scales with a* and almost contributes to the total drag force. When a*>1.0, the added mass force scaling with a* contributes to most of the drag force. Furthermore, the two force generation mechanisms associated with acceleration (a*) are independent, and a criterion based on the energy ratio is proposed to identify the transition of the two force generation mechanisms. The present results uncover the role of acceleration in force generation and explain the inconsistencies of using one quasi-steady model in describing the force on accelerating plates.

Natural convective solar dryer powered by stepped fin plate integrated trough array solar air heater for agricultural produce preservations

In this work, heat energy analysis and economic feasibility of natural convection mixed mode solar dryer under three different methods viz., normal flat plate collector solar dryer (NFPSD), step fin plate integrated trough array collector solar dryer (SFPTSD) and SFPTSD with latent heat storage (LHS) are experimentally investigated. The drying time in SFPTSD – LHS (setup 3) to reach its safe moisture content for paddy, wheat, green chilli are 5.5 h, 6 h and 7 h respectively and it is significantly lowered to a maximum of 47 % as compared with NFPSD (setup 1). Also, the average maximum heat efficiency of 62.19 % for collector and 38.32 % for drying cabinet is obtained in setup 3. The specific heat energy consumption is lowered by 20.65 % and specific moisture extraction rate increases to 21.73 % for this proposed setup in comparison with setup 1. The improvement potential is reduced to a substantial margin of 136.5 W and yields an exergetic efficiency increase of 12.38 % than setup 1. An average annual saving increase of 193.08$ with its present value 94.33$ is achieved for setup 3 as compared with setup 1. We recommend this setup can dry edible produce at low cost and affordable to economically weak farming communities.

Detached-Eddy Simulation of Normal Flow past Flat Plates: The Influence from Corner Curvature

Detached-Eddy Simulation of Normal Flow past Flat Plates: The Influence from Corner Curvature

Exploring the influence of span-wise boundary conditions on the wake of a thin flat plate using Fourier-Averaged Navier–Stokes equations

The wake of a thin normal flat plate with different end conditions is numerically analyzed at a Reynolds number of 250. Periodic, slip, and no-slip boundary conditions are considered for the spanwise boundaries in order to analyze the effect of spanwise flow constraints using a new technique: Fourier-Averaged Navier–Stokes equations (FANS). The results of cases with periodic and slip end conditions were similar in both mean and unsteady fields. However, no-slip boundary conditions, which could represent the case of experimental setups with end plates, significantly reduce the velocity, drag and lift fluctuations in the flow. FANS analysis confirmed that loss of the nominal two-dimensional behavior due to the no-slip end condition relates to the presence of a spanwise flow coherence at the vortex shedding frequency (mode). Interactions between the rollers and boundary layer induces large-scale spanwise fluctuations that are absent without the end plates. In this way, the boundary layer due to the end plate serves as a flow control mechanism that suppresses fluctuations in the flow and reduces stresses in the center-plane, alongside increasing coherence in the spanwise flow.

Comparison of Edge Vortices from Normal and Elliptic Flapping Flat Plates

Computational analysis of elliptic and normal flat plate geometries, sized to wings of small fliers and in a two-dimensional plunging–pitching–flapping motion resulting in hover, is conducted to investigate circulation growth at the leading-edge vortex (LEV) and trailing-edge vortex (TEV). The models are sized to the same aspect ratio, and a Reynolds number of 225 is chosen as it is similar to that observed in small fliers in hover. Results show similar LEV growth and lift production trends for both cases but with differing energy flux mechanisms. A vorticity transport analysis is done to quantify these energy fluxes. The LEV growth and shearing is closely related to the TEV growth and shearing, and the plunging–pitching profile, while the geometry plays a role in the magnitude of vortex creation and intensity of spanwise fluxes only.

Planar shear flow effects on particle dispersion over a normal flat plate

Planar shear flow effects on particle dispersion over a normal flat plate

Perforation effects on the wake dynamics of normal flat plates

The effect of perforation on the wake of a thin flat plate placed normal to the free stream at Reynolds number ( $Re$ ) 250 (based on plate width $d$ , and inflow velocity $U_o$ ) is studied by means of direct numerical simulation. The perforated plate of length $6d$ consist of six equidistant square holes of varying sizes corresponding to porosity $\beta$ (ratio of open area to total plate area) of 0 %, 4 %, 9 %, 12.25 %, 16 %, 20.25 % and 25 %. It is observed that the bleed or jet flow through perforations pushes the shear layer interaction farther downstream with increasing $\beta$ . This causes a monotonic decrease in the drag coefficient with increasing porosity, and a sharp fall seeming to begin at $\beta \approx 4\,\%$ . On the other hand, the Strouhal number increases with $\beta$ up to 16 % (at $\beta =16\,\%$ , loss of flow three-dimensionality leads to a ‘quasi-laminar’ state of flow). This is followed by a sharp fall in the Strouhal number at $\beta \approx 20\,\%$ . The behaviour of the large-scale vortical structures in the far wake is influenced by the near-wake behaviour of the bleed flow, where the local $Re$ based on the perforation hole size determines the overall flow three-dimensionality. It is also observed that the jet or bleed flow undergoes meandering instability when pitch separation is equivalent to the hole size (at $\beta =25\,\%$ ). The low- $Re$ turbulent flow for a non-perforated plate is altered to a transitional state by the presence of perforation. The streamwise vortex pairs (secondary instabilities) become fairly organized as $\beta$ is increased from 0 % to 16 %. The secondary instability at $\beta =16\,\%$ appears similar to mode-B with wavelength ${\approx }1d$ . On the contrary, the secondary instability at $\beta =25\,\%$ appears similar to mode-A with a wavelength of ${\approx }2d$ .

Three-Dimensional Numerical Simulation of a Flat Plate Perpendicularly Submitted to Current With a Blockage Ratio of 0.214: URANS and Detached Eddy Simulation

Abstract The uniform flow over a nominally two-dimensional normal thin flat plate with blockage ratio 0.214 was numerically investigated in three dimensions by three methods: unsteady Reynolds-averaged Navier–Stokes (URANS) based on the realizable k–epsilon (RKE) turbulence model, URANS based on the k–omega shear stress transport (SST) turbulence model, and detached eddy simulation (DES). The Reynolds number based on the inlet flow velocity and the chord width of the plate was 117,000. A comprehensive comparison against earlier experimental results showed that URANS-SST method only could give a correct Strouhal number but overestimated the mean base pressure distribution and mean drag coefficient, while URANS-RKE and DES methods succeeded in giving accurate predictions of all. Moreover, by comparing the instantaneous vorticity contours and three-dimensional (3D) turbulent flow structures, it is found that DES is better suited for the present case because it can capture irregular small-scale structures and reproduce the three-dimensionality and low-frequency unsteadiness of the vortex shedding. Finally, through the volume-of-fluid (VOF)-based simulation of the free surface, it is demonstrated that the free surface has no significant effect on the mean drag coefficient and Strouhal number.

CHARACTERISTICS OF WAKE TURBULENCE GENERATED BY A NORMAL FLAT PLATE

CHARACTERISTICS OF WAKE TURBULENCE GENERATED BY A NORMAL FLAT PLATE

On the three-dimensional wake flow behind a normal flat plate

Two-dimensional (2D) and three-dimensional (3D) numerical simulations are carried out for uniform flow past a normal flat plate with two semicircular ends to investigate the three-dimensional effects of the wake flow behind the plate. The Reynolds numbers under investigation based on the inflow velocity and the width of the plate (H) are Re= 125, 200, 250, 500, and 1000. The instantaneous vortical structures show that the three-dimensionality characterized by streamwise vortical ribs becomes obvious at Re=200. Their spatial densities increase with the increasing Re. The time-averaged drag coefficient remains almost the same from Re=500 to 1000. The relative difference of the predicted drag coefficients between 2D and 3D simulations can be up to 77%. The amplitude of the lift force obtained using 2D simulations can be up to 30 times that obtained using 3D simulations. A drag force element decomposition analysis is conducted for the results obtained using 2D and 3D simulations. It is found that although the time-averaged wake flows obtained using the 2D and 3D simulations are different, the relative difference of their contributions to the time-averaged drag coefficient is only 10% while the difference comes mainly from the contribution of the Reynolds shear stress. The three-dimensionality of the wake flow is further investigated using quadrant and the Lumley triangle analysis of the Reynolds stress. The spanwise spatial scales of the streamwise vortices are quantified using Hilbert transform along the spanwise direction. The width of the streamwise vortices is approximately 0.5–1H in the near wake region. The dependence of the spatial scales on Re is discussed.

Onset of vortex shedding from a bluff body modified from square cylinder to normal flat plate

This study numerically investigates the time-resolved laminar flow over rectangular cylinders with cross-sectional aspect ratio Ar varying from square cylinder (Ar = 1) to normal flat plate (Ar = 0.1) for Reynolds number Re = 40–100. The focus is given on how Ar influences the wake structure, fluid force, St, and critical Reynolds number Rec associated with the onset of vortex shedding. The Stuart-Landau equation is employed to determine Rec. With increasing Re, time-mean drag coefficient C‾D increases and decreases for Ar < 0.5 and Ar > 0.5, respectively. The Re effect on C‾D is strongest for Ar = 0.1 and weakest for Ar = 0.5. On the other hand, St monotonically increases with Re for all Ar values examined. Both C‾D and St at a given Re diminish with increasing Ar. A decrease in Ar from 1.0 to 0.1 destabilizes the flow, reducing the Rec from 47.8 to 29.8. The dependence of Rec on the flow attack angle α = (0° - 45°) for the square cylinder shows Rec declining from Rec = 47.8 at α = 0° to Rec = 40.2 at α = 45°. A comparison of Ar effects on Rec is made between rectangular (present study) and elliptical cylinders, both changing toward the normal flat plate. The rectangular cylinders have a smaller Rec than the elliptical cylinders for Ar < 1 while the opposite is the case for Ar = 1.

Thermo-fluid dynamic analysis in a micro-textured evaporator based on microscale infrared/visible observations for loop heat pipes

This paper presents a thermo-fluid dynamic analysis in a micro-textured evaporator for loop heat pipes (LHPs) that has a super wetting surface with ethanol on the basis of an experiment and modeling. In the experiment, three kinds of stainless steel plates with various morphologies of heat transfer surfaces were tested: a normal flat plate, a sandblasted plate, and a micro-groove plate. The measured contact angles between the surfaces and ethanol were 8.2° ± 1.3°, 0°, and 0°, respectively. Evaluation of the heat transfer performance and liquid-vapor interface behavior was conducted using microscale infrared and visible observations. As a result, it was revealed that the sandblasted plate and the micro-groove plate showed 7 times and 20 times higher heat transfer coefficient under high heat flux conditions respectively, compared with the normal flat plate. Different liquid-vapor interface behaviors were found between the plate types. In the modeling, the heat transfer coefficient was predicted for each case. It was found that nucleate boiling heat transfer induced by rough surface increased the heat transfer performance in the case of the sandblasted plate. In addition, it was revealed that the thin film evaporation at the long triple-phase contact line significantly enhanced heat transfer performance in the case of the micro-groove plate. The findings indicate a new promising approach to enhance the heat transfer coefficient of LHP evaporators.

Dynamic heat transfer model of flat plate solar water collectors with consideration of variable flow rate

The dynamic thermal model of the collector could serve as a useful tool for the thermal prediction. Normally, collectors’ thermal prediction models are developed based on the dynamic thermal process, and then the thermal output or the mean temperature of the fluid would be obtained from the mathematical derivation. The critical parameters in the equations are fitted from the test data. In which, the heat loss coefficient F′UL has a close relationship with the flow rate, and thus the fitting formula could only be used for a given flow rate. In this paper, a dynamic heat transfer model of the normal flat plate solar collector is introduced, with consideration of the mass flow rate variations. Matrix is employed for solving the heat transfer equations. The analytical solution of the model indicates that the temperatures at timeτ are determined by the initial value and the accumulated effect of the ambient environment. The model is validated by the on-site experiment carried out in Zhangjiakou, Hebei Province, in the north part of China. The main trend of the simulation and measurement was in accordance continually in the initialization, operation, and halt phase for around 24 h. While, the thermal mass of the duct connected to the collector is not included in the model, leading to the accuracy reduction of the model prediction. The modification with consideration of the pipeline’s thermal mass will be conducted in future work.

Elastic buckling analysis of rectangular longitudinally profiled (LP) steel plates under uniform compression

Longitudinally profiled (LP) steel plates are plates rolled to variable thickness along the rolling direction in order to suit practical loading distributions in construction applications. The elastic buckling load of LP steel plates is different to normal flat plates due to the change in thickness and it is hard to find analytical solutions to the governing equation. In this paper, the elastic buckling coefficients of rectangular LP plates were calculated using the Galerkin and Rayleigh-Ritz method (GRM). The plates were under uniform compression and four typical boundary conditions were considered. The element expression of the feature matrix was obtained by theoretical derivation and the elastic buckling coefficients were obtained by calculating the eigenvalues of the feature matrix numerically with MATLAB. Numerical models of LP plates were developed to validate the derivation. Upon validation it was further found that the elastic buckling coefficients of LP plates can be approximately expressed by those of constant thickness steel plates together with variable thickness coefficients. A series of approximation formulae of elastic buckling coefficients of LP rectangular steel plates were proposed. Simplified design formulae of elastic buckling coefficients of LP plates were proposed for the first time to promote the application of LP plates in engineering practice.

Experimental Investigation of Thermal Performance Evaluation of Solar Flat Plate Collector

A flat plate collector is a simple and widely used device for space heating, domestic and industrial hot water applications. In this study, a device is fabricated and installed in Sultanpur for conducting experiments on flat plate collector to obtain the collector efficiency, rate of fluid heating and cooling and the temperature difference of fluid at inlet and outlet of the collector. The study made an attempt to enhance efficiency as compared to the normal flat plate collector by improving the collector design and varying the tilt angle, and mass flow rates. From the experiments, it was concluded that the efficiency is directly proportional to mass flow rate and inversely proportional to the wind speed. It was also found that factor like plate absorptive, glass cover emissivity, number of the glass cover and tilt angle and atmospheric condition affect the performance of flat plate collector.

The Impact Force Acting on a Normal Flat Plate Due to Non-Continuum Flow Issuing from Planner Exit with Different Speed Ratio

This paper analysed the impact forces acting on a flat plate exposed normally to a rarefied plume issuing from a nozzle with a planner exit. The plate is assumed to be completely diffuse and the gaseous plume flow out of the exit is modelled with a Maxwellian distribution function, which was characterized with known number density, nonzero exit velocity, and temperature. The analytical collisionless flow results for drag force and shear force due to the impingement on the plate were derived. Effects of speed ratio, wall temperature, exit plume temperature, plate length and vertical distance between nozzle exit and plate center in the impact forces were studied. The results showed that the drag or shear force was directly proportional to the surface area of the flat plate. The drag and shear force increased as the speed ratio increased up to plate semi width of 0.7 m, then both forces decreased as the speed ratio increased up to the end of the plate length. The drag or shear force increased as the distance between the plate and nozzle exit decreased. In addition, the drag force increased as the plume exit temperature or plate temperature increased, while the shear force increased as the plume exit temperature increased. In considering the reflected particles from the plate or neglecting these particles; shear force was not affected, while drag force decreased when the reflected particles were neglected from the computation. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solution for the surface pressure, shear stress distributions, and the impact forces.

Performance of Turbulence Models in Simulating Wind Loads on Photovoltaics Modules

The performance of five conventional turbulence models, commonly used in the wind industry, are examined in predicting the complex wake of an infinite span thin normal flat plate with large pressure gradients at Reynolds number of 1200. This body represents a large array of Photovoltaics modules, where two edges of the plate dominate the flow. This study provided a benchmark for capabilities of conventional turbulence models that are commonly used for wind forecasting in the wind energy industry. The results obtained from Reynolds Averaged Navier-Stokes (RANS) k - ε , Reynolds Normalization Group (RNG) k - ε , RANS k - ω Shear Stress Transport (SST) and Reynolds Stress Model (RSM) were compared with existing Direct Numerical Simulations (DNS). The mean flow features and unsteady wake characteristics were used as testing criteria amongst these models. All turbulence models over-predicted the mean recirculation length and under-predicted the mean drag coefficient. The major differences between numerical results in predicting the mean recirculation length, mean drag and velocity gradients, leading to deficits in turbulence kinetic energy production and diffusion, hint at major difficulties in modeling velocity gradients and thus turbulence energy transport terms, by traditional turbulence models. Unsteadiness of flow physics and nature of eddy viscosity approximations are potential reasons. This hints at the deficiencies of these models to predict complex flows with large pressure gradients, which are commonly observed in wind and solar farms. The under-prediction of wind loads on PV modules and over-estimation of the recirculation length behind them significantly affects the efficiency and operational feasibility of solar energy systems.

Wake dynamics and surface pressure variations on two-dimensional normal flat plates

The relationship between vortex dynamics and surface pressure fluctuations on the leeward face of a two-dimensional normal thin flat plate was studied using Direct Numerical Simulations for incompressible flow at a Reynolds number of 1200. The vortex shedding frequency was observed in the spectra of pressure fluctuations on both faces of the plate, while a lower frequency spectral peak was only evident on the leeward pressure fluctuations. Local sharp peaks of low pressure in the separated shear layers coincide with increases in the leeward face pressure fluctuations. These observations are tied to the vortex dynamics using the invariant Q, commonly used for vortex identification. Q is also proportional to the source term for the Poisson equation for the instantaneous pressure. The pressure, which is the only contributor to the plate drag, varies significantly in response to alterations to the vortex shedding, which can be observed in differences of vortex trajectories. At minimum drag, the pressure fluctuations are small, which is attributed to lower values of Q associated with weaker vortices.

Drag force on an accelerating submerged plate

We present results on the drag on, and the flow field around, a submerged rectangular normal flat plate, which is uniformly accelerated to a constant target velocity along a straight path. The plate aspect ratio is chosen to be$AR=2$to resemble an oar blade in (competitive) rowing, the sport which inspired this study. The plate depth, i.e. the distance from the top of the plate to the air–water interface, the plate acceleration and the plate target velocity are varied, resulting in a plate width based Reynolds number of$4\times 10^{4}\lesssim Re\lesssim 8\times 10^{4}$. In our analysis we distinguish three phases; (i) the acceleration phase during which the plate drag is enhanced, (ii) the transition phase during which the plate drag decreases to a constant steady value upon which (iii) the steady phase is reached. The plate drag force is measured as function of time which showed that the steady-phase plate drag at a depth of$1/5$plate height (20 mm depth for a plate height of 100 mm) increased by 45 % compared to the plate top at the surface (0 mm). Also, it is shown that the drag force during acceleration of the plate increases over time and is not captured by a single added mass coefficient for prolonged accelerations. Instead, an entrainment rate is defined that captures this behaviour. The formation of starting vortices and the wake development during the time of acceleration and transition towards a steady wake are studied using hydrogen bubble flow visualisations and particle image velocimetry. The formation time, as proposed by Gharibet al.(J. Fluid Mech., vol. 360, 1998, pp. 121–140), appears to be a universal time scale for the vortex formation during the transition phase.

A framework to develop data-driven turbulence models for flows with organised unsteadiness

Turbulence modelling development has received a boost in recent years through assimilation of machine learning methods and increasing availability of high-fidelity datasets. This paper presents an approach that develops turbulence models for flows exhibiting organised unsteadiness. The novel framework consists of three parts. First, using triple decomposition, the high-fidelity data is split into organised motion and stochastic turbulence. A data-driven approach is then used to develop a closure only for the stochastic part of turbulence. Finally, unsteady calculations are conducted, which resolve the organised structures and model the unresolved turbulence using the developed bespoke turbulence closure. A case study of a wake with vortex shedding behind a normal flat plate, at a Reynolds number of 2,000, based on plate height and freestream velocity, is considered to demonstrate the method. The approach shows significant improvement in mean velocity and Reynold stress profiles compared with standard turbulence models.