Flat Plate Of Finite Thickness Research Articles

Low-frequency still-air acoustic inertia of inclined circular aperture in an infinite flat plate of finite thickness

The acoustic inertia of the canonical configuration of inclined circular aperture(s) in a finite-thickness plate at the low frequency limit is investigated under the inviscid still-air condition. A hybrid approach combining modal expansion and boundary element method is applied to calculate the effective length of the aperture as a quantitative characterisation of its acoustic inertia. These calculations, covering different inclination angles up to 75°, are performed for a single isolated aperture with a selected range of plate thickness and the periodic aperture arrays of aligned and staggered arrangements with a selected range of aperture spacing respectively. The results are validated by the simulations carried out with the commercial software COMSOL. The parametric studies of geometric dimensions included in this work provide representative results for typical acoustic related engineering applications of finite-length inclined apertures. A link for access to the MATLAB programmes implementing the calculations is provided for interested readers. As an example of application, the hybrid method described in this work is used for the acoustic modelling of a representative multi-perforated liner studied in the literature for the problem of thermo-acoustic instability. The results compared well against those obtained from the Computational Fluid Dynamics simulations reported in the literature.

Dusty Gas Flow past Bodies under Scattering of Rebounded Particles

Two-phase gas-particle flow over a flat plate of finite thickness in a channel at a high subsonic velocity and supersonic transverse flow past a cylinder are considered. The leading edge of the plate is wedge-shaped or represents a smooth bluntness of constant radius. The wedge surface and the front bluntness are specified both smooth and rough. The roughness is modeled by a two-dimensional profile based on an experiment. Spherical particles and a mixture of particles in the form of ellipsoids of revolution, rectangular prisms, prisms with flat-cut vertices, and tetrahedrons are considered. The parameters of each of the forms vary. The impact interaction model proposed earlier and consistent with the experimental data on the coefficients of restitution of the center-of-mass velocity is used to determine the translational and rotational velocities of non-spherical particles after rebound. Along with monosized particles, a dispersed phase with a spread of particles in size is considered. The role of the studied factors of random nature which affect the flow pattern and the dispersed phase parameters is found.

Transient Heat Transfer Analysis on Composite Solids for Hypersonic Flow Applications

Surface heating rates have the importance in high speed flow due to viscous or aerodynamic heating which leads to enormous rise in surface temperature. Prediction of exact heat transfer rates is essential for design of protection systems for aerodynamic bodies aimed. For the thermal protection system, the aerodynamic Surfaces are generally configured with multiple solids. Hence present study is planned to develop the conjugate heat transfer (CHT) solver for composite solids. A CHT solver is in hypersonic flow environment. Finite volume framework and explicit time stepping have been implemented for both the compressible Navier-Stokes solver and conduction solver. Loose coupling has been established between the above mentioned fluid and solid domain solvers. The following observations were made in the CHT simulations. In the case of hypersonic flows over finite thickness flat plate, considerable difference in surface heat transfer rate has been noticed along the stream wise direction at the solid-fluid interface and also the Effect of wall material on heat diffusion for hypersonic application has been analyzed using loosely coupled CHT solver. The CHT solver has also been implemented for hypersonic flow over composite cylinder. Necessity of insulating material in the region of stagnation point has been realized as the outcome of these studies.
 HIGHLIGHTS
 
 Accurate prediction of Convective heating rates is essential for the design of thermal protection system for hypersonic vehicles
 In The thermal protection system, the aerodynamic surfaces are generally configured with multiple solids. Hence the present study is planned to develop the conjugate heat transfer (CHT) solver for composite solids
 The CHT solver has been implemented for hypersonic flow over composite flat plate and cylinder. It has been observed flows over finite thickness flat plate, a considerable difference in surface heat transfer rate has been noticed along the stream wise direction at the solid-fluid interface and the necessity of insulating material in the region of stagnation point has been realized as the outcome of these studies
 
 GRAPHICAL ABSTRACT

Effect of Mach number and plate thickness on the flow field and heat transfer characteristics of supersonic turbulent flow over a flat plate at different thermal boundary conditions

Conjugate heat transfer analysis of supersonic turbulent flow over a finite thickness flat plate is studied numerically. The flow field is modeled by employing the Favre averaged Navier–Stokes (FANS) equations. Turbulence is modeled with the Menter’s shear-stress-transport (SST) k−ω model. The comparison of NCHT (non-conjugate heat transfer) and CHT (conjugate heat transfer) analysis shows that the interface temperature and fluid temperature variation for the CHT analysis are lower compared to the NCHT analysis. The results indicate that the interface temperature is significantly increased for the low thermal conductivity plate material, due to the reduced rate of heat transfer. The effect of plate thickness on the flow field temperature variation is negligible. However, it is observed that the maximum interface temperature Ti,max increases with the increase in plate thickness. The values of maximum interface temperature difference between the 5 mm and 2 mm thick Steel-1006 plates at Mach numbers 2, 4, and 5 in non-dimensional (non-dimensionalized with free-stream temperature) form are 0.05594, 0.129, and 0.1816 respectively for the isothermal boundary condition. Results indicate that for Mach 2, the heated wall thermal boundary conditions acts like heat source, leading to the higher interface temperature, whereas for Mach 4, and 5 the heated wall thermal boundary conditions acts like heat sink, thus lowering the interface temperature. The results show that for NCHT analysis the leading edge shock strength, and mean pressure along the wall increases with an increase in Mach number. The non-conjugate results (flow and heat transfer characteristics) of the present numerical study is validated with the direct numerical simulation (DNS) results available in the literature.

Conjugate heat transfer study of a turbulent slot jet impinging on a moving plate

Numerical simulation of the flow field and conjugate heat transfer in an impinging jet with moving impingement plate is one of the important problems as it mimics closely with practical applications in industries. The Yang–Shih version of low Reynolds number k– $$\epsilon$$ model has been used to resolve the flow field and the temperature field in a two-dimensional, steady, incompressible, confined, turbulent slot jet impinging normally on a moving flat plate of finite thickness. The turbulence intensity and the Reynolds number considered at the inlet are $$2\,\%$$ and 15,000, respectively. The bottom face of the impingement plate has been maintained at a constant temperature higher than the nozzle exit temperature. The confinement plate has been considered to be adiabatic. The nozzle-to-surface spacing for the above study has been taken to be 6 and the surface-to-jet velocity ratios have been taken over a range of 0.25–1. The effects of impingement plate motion on the flow field and temperature field have been discussed elaborately with reference to stationary impingement plate. The dependence of flow field and fluid temperature field on impingement plate motion has been analyzed by plotting streamlines, isotherms for different plate speeds. A thorough study of flow characteristics for different surface-to-jet velocity ratios has been carried out by plotting profiles of mean vertical and horizontal components of velocity, pressure distribution, local shear stress distribution. The isotherms in the impingement plate of finite thickness, the distributions of solid–fluid interface temperature, the local Nusselt number, and the local heat flux for different surface-to-jet velocity ratios added to the understanding of conjugate heat transfer phenomenon.

Acoustic receptivity simulations of flow past a flat plate with elliptic leading edge

We present results of numerical simulations of leading-edge acoustic receptivity for acoustic waves impinging on the leading edge of a finite-thickness flat plate. We use both compressible and incompressible flow solvers fitted with high-order high-accuracy numerical methods and independent methods of estimating the receptivity coefficient. The results show that the level of acoustic receptivity in the existing literature appears to be one order of magnitude too high. Our review of previous numerical simulations and experiments clearly identifies some contradictory trends. In the limit of an infinitely thin flat plate, our results are consistent with asymptotic theory and numerical simulations.

Conjugate Heat Transfer Study of Turbulent Slot Impinging Jet

Conjugate heat transfer in a two-dimensional, steady, incompressible, confined, turbulent slot jet impinging normally on a flat plate of finite thickness is one of the important problems as it mimics closely with industrial applications. The standard high Reynolds number two-equation k–ε eddy viscosity model has been used as the turbulence model. The turbulence intensity and the Reynolds number considered at the inlet are 2% and 15,000, respectively. The bottom face of the impingement plate is maintained at a constant temperature higher than the jet exit temperature and subjected with constant heat flux for the two cases considered in the study. The confinement plate is considered to be adiabatic. A parametric study has been done by analyzing the effect of nozzle-to-plate distance (4–8), Prandtl number of the fluid (0.1–100), thermal conductivity ratio of solid to fluid (1–1000), and impingement plate thickness (1–10) on distribution of solid–fluid interface temperature, bottom surface temperature (for constant heat flux case), local Nusselt number, and local heat flux. Effort has been given to relate the heat transfer behavior with the flow field. The crossover of distribution of local Nusselt number and local heat flux in a specified region when plotted for different nozzle-to-plate distances has been discussed. It is found that the Nusselt number distribution for different thermal conductivity ratios of solid-to-fluid and impingement plate thicknesses superimposed with each other indicating that the Nusselt number as a fluid flow property remains independent of solid plate properties.

Conjugate Forced Convection Heat Transfer From a Heated Flat Plate of Finite Thickness and Temperature- Dependent Thermal Conductivity

In this paper, a conjugate forced convection heat transfer from a good conducting plate with temperature-dependent thermal conductivity is studied. The semi-analytical solution for the nonlinear integro-differential equation occurring in the problem is handled easily and accurately by implementing the differential transform method (DTM). The horizontal plate is heated with uniform heat flux at the lower surface while being cooled at the upper surface under laminar forced convection flow. A numerical approach is also performed via a finite-volume method to examine the validity of the results obtained by DTM. The results of DTM show closer agreement with the results of the numerical method than the results obtained by the perturbation method existing in the literature. It is concluded that for a good conducting plate with a finite thickness the distribution of the conjugate heat flux at the upper surface is significantly affected by the plate thickness. Moreover, we conclude that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the nonconjugate case.

An Experimental Study on the Effect of Submergence on a Vertically Oscillating Hydrofoil at Zero Translational Velocity

This paper presents experimental results for the hydrodynamic forces on several different bodies oscillating in the vicinity of the free surface. Firstly, results for two horizontally symmetric bodies, a flat plate of finite thickness and a cylinder, are presented. Results show that these two different shaped bodies react in different ways with the free surface and are likely to have different added mass associated with them. Secondly, results for two thrusting bodies, a NACA0012 symmetrical foil and a NACA4415 cambered foil, show that the free surface amplifies the thrust produced by a vertically oscillating foil. Results showing the effects of spanwise flow are also presented and indicate spanwise flow is negligible at zero translational velocity and so the use of endplates of the foils was unnecessary. The conclusion of these experiments is that a submergence of 5 chord lengths is sufficient for the horizontal and vertical forces on the vertically oscillating objects to be unaffected by the free surface.

Conjugate Heat-Transfer Analysis for Hypersonic Flow over Finite Thickness Flat Plate

AbstractImplementation of the conjugate heat-transfer (CHT) analysis technique for hypersonic applications is the central theme of the present investigations. Understanding the applicability of the assumptions used in heat-transfer measurements and wall material-based flowfield analysis are the major objectives of the present studies. In view of this, a special CHT solver is developed for these investigations. This 2D-solver is based on explicit finite-volume formulation for fluid domain and implicit finite volume formulation for solid domain computations. The present numerical explorations are carried out using this in-house solver for various wall materials, different freestream Mach numbers, and freestream stagnation enthalpies of hypersonic flows over a finite thickness flat plate. Encouraging match has been observed between the results obtained from the CHT solver for very high thermal conductivity wall case and present fluid flow solver for isothermal flat plate case. Viability of assumptions used f...

Evaluation of Reynolds number effects on flutter derivatives of a flat plate by means of a computational approach

Abstract This paper proposes an efficient method to determine the flutter derivatives of two-dimensional streamlined cylinders by means of a modified indicial approach adapted to a Navier–Stokes solver using an Arbitrary Lagrangian Eulerian formulation. The method relies on heave or pitch motion imposed on the structure according to smoothed-ramp-time histories and on the computational evaluation of the transient forces that arise on the obstacle. Hence, the indicial transfer function that relates the structural motion to the induced force in the frequency domain is obtained. The approach is applied to a flat plate of finite thickness and length immersed in a viscous flow. The low computational costs of the method allow the effects of Reynolds number to be evaluated on both the aerodynamic and aeroelastic behaviour for a wide range of Re values. The flow around the motionless plate is compared to the well-known Blasius and Goldstein solutions. The flutter derivatives extracted from simulations with a moving plate are compared to ones obtained from the Theodorsen function in the frame of the thin airfoil theory. Relationships between the variation of Re, the fluid flow phenomena and the flutter derivatives are highlighted in order to identify the flow field features that affect the flutter derivatives to the greatest extent.

Experimental Validation of Analytical Solutions for Vertical Flat Plate of Finite Thickness Under Natural-Convection Cooling

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter (α) during various test conditions were 2×108–6×108, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is observed between the experimental and analytical results.

Determination of the aeroelastic transfer functions for streamlined bodies by means of a Navier–Stokes solver

This paper proposes a method to determine the flutter derivatives of two-dimensional streamlined cylinders by means of a modified indicial approach adapted to a Navier–Stokes solver using an Arbitrary Lagrangian Eulerian formulation. The method relies on heave or pitch motion imposed onto the section according to smoothed-ramp time-histories and on the computational evaluation of the transient forces arising on the obstacle. Hence, the indicial transfer function relating the plate motion to the induced force in the frequency domain is obtained. Application to a flat plate of finite thickness and length is proposed. The steady viscous flow simulated around the motionless plate is compared with the well-known Blasius solution. The computed flutter derivatives are compared both with those obtained from the Theodorsen function in the frame of the thin airfoil theory and with those resulting from previous methods in the frame of the computational approach.

Thermal capacity effect on transient free convection adjacent to a vertical surface in a porous medium

In this paper we analyse how the presence of the thermal capacity of a vertical flat plate of finite thickness, which is embedded in a porous medium affects the transient free convection boundary-layer flow. At the time t = 0, the plate is suddenly loaded internally with a constant heat flux rate q″, so that a transient boundary-layer flow is initiated adjacent to the plate. Initially, the transient effects due to the imposition of the uniform heat flux rate at the plate are confined to a thin fluid region near to the surface and are described by a small time solution. These effects continue to penetrate outwards and eventually evolve into a new steady state flow. Analytical solutions have been derived for these transient (small time) and steady state (large time) flow regimes, which are then matched by a numerical solution of the full boundary-layer equations. It has been found that the non-dimensional fluid temperature (or fluid velocity) profiles are reduced when the thermal capacity effects, described by a parameter Q *, are reduced. For small values of Q *, the approach of these profiles to their steady state values is monotonic. However, for large values of Q *, the temperature profiles are observed to locally exceed (pass through a maximum value) the final steady state values at certain distances from the plate. In general, the maxima in the temperature profiles increase in size as Q * increases and the time taken to approach the steady state solutions increases significantly.

An experimental study of large-scale vortices over a blunt-faced flat plate in pulsating flow

Laboratory measurements are made of flow over a blunt flat plate of finite thickness, which is placed in a pulsating free stream, U=U o (1+A o cos 2πfpt). Low turbulence-intensity wind tunnel experiments are conducted in the ranges of Stp≤1.23 and A o ≤0.118 at ReH=560. Pulsation is generated by means of a woofer speaker. Variations of the time-mean reattachment length xR as functions of Stp and A o are scrutinized by using the forward-time fraction and surface pressure distributions (Cp). The shedding frequency of large-scale vortices due to pulsation is measured. Flow visualizations depict the behavior of large-scale vortices. The results for non-pulsating flows (A o =0) are consistent with the published data. In the lower range of A o , as Stp increases, xR attains a minimum value at a particular pulsation frequency. For large A o , the results show complicated behaviors of xR. For Stp≥0.80, changes in xR are insignificant as A o increases. The shedding frequency of large-scale vortices is locked-in to the pulsation frequency. A vortex-pairing process takes place between two neighboring large-scale vortices in the separated shear layer.

Surface temperature of a flat plate of finite thickness under conjugate laminar forced convection heat transfer condition

Surface temperature of a flat plate of finite thickness under conjugate laminar forced convection heat transfer condition

Flow and mass transfer measurements for a flat plate of finite thickness in pulsating flow

Laboratory measurements were made of flow and mass transfer over a blunt flat plate of finite thickness, which is placed in a pulsating free stream, U x = U 0 (1+ A 0 cos 2 πƒ p t). Low turbulence-intensity wind tunnel experiments were conducted for small and moderate Reynolds numbers, 770 ⩽ Re H ⩽ 8000. Pulsation was generated by means of an acoustic speaker. The majority of experiments were carried out in the ranges of ƒ p = 20.0–80.0 Hz and A 0 ⩽ 0.15. Flow properties were measured by I-type and split-film probes. Mass transfer rates were measured by employing the naphthalene sublimation technique. The present results for non-pulsation flows ( A 0 = 0.0) were shown to be consistent with the published data. For pulsating approach flows, results are provided for the distributions of the wall static pressure, the longitudinal mean velocity and turbulent intensity, and the Sherwood number, Sh, as a function of the stream-wise distance x * measured from the leading-edge separation point. As A 0 or ƒ p increases, the time-mean reattachment length is reduced significantly. This implies that the height and length of the separation bubble shrink simultaneously: the position where C p is recovered moves upstream, and the minimum value of C p decreases; the reverse flow is intensified: and a substantial augmentation of turbulent energy is discernible. In the separation bubble, the effect of pulsation on Sh is conspicuous. Sh decreases monotonically from the separation point to the minimum value near the secondary separation point; and Sh increases appreciably with increasing x *, after passing the secondary separation point to the maximum value at the reattachment point; and afterward, Sh decreases. The secondary separation point and the position where Sh has a maximum move further upstream, as A 0 or ƒ p increases. At large Re H, the relative influence of pulsation on Sh weakens.

Heat and mass transfer from a flat plate of finite thickness to a boundary layer flow with transpiration

Cooling a flat plate by evaporation of a volatile liquid from the surface to a laminar boundary layer flow past the plate is theoretically analyzed, taking into account both injection effect due to the vaporization and two-dimensional thermal conduction in the plate, with convective thermal-boundary condition on the other plate surface. The thermal effect of the volatile liquid supply to the plate is neglected and all of the physical properties are assumed to be constant in spite of the changes in concentration and temperature in the boundary layer. Representative calculations were performed for air-water system with various thermal conditions of the plate and flow conditions. The temperature fields and distributions of the local Nusselt and Sherwood numbers are estimated for a parallel flow case. The effects of parameters related to the wall conduction on the injection parameter are discussed. Comparison of results calculated for air-methanol and air-water systems shows that in the former case the injection gives more significant influence on the heat and mass transfer characteristics.

Two dimensional discrete vortex method for application to bluff body aerodynamics

Abstract Two-dimensional viscous incompressible flow past a flat plate of finite thickness and length is simulated using the discrete vortex method. Both a fixed plate and a plate undergoing a harmonic heave and pitch motion are studied. The Reynolds number is 104 and the record onset flow speed, U fc is in the range 2–14. The fundamental kinematic relation between the velocity and the vorticity is used in a novel approach to determine the surface vorticity. An efficient influence matrix technique is used in a fast adaptive multipole algorithm context to obtain a mesh-free method. The numerical results are compared with the steady-state Blasius solution, and with the inviscid solution for the flow past an oscillating plate by Theodorsen.

Parallel Monte Carlo simulation of three-dimensional flow over a flat plate

This article describes a parallel implementation of the direct simulation Monte Carlo (DSMC) method. Runtime library support is used for scheduling and execution of communication between nodes, and domain decomposition is performed dynamically to maintain a favorable load balance. Performance tests are conducted using the code to evaluate various remapping and remapping-interval policies, and it is shown that a onedimensional chain-partitioning method works best for the problems considered. The parallel code is then used to simulate the Mach 20 nitrogen flow over a finite thickness flat plate. It will be shown that the parallel algorithm produces results that are very similar to previous DSMC results, despite the increased resolution available. However, it yields significantly faster execution times than the scalar code, as well as very good load-balance and scalability characteristics.