Length Of Flat Plate Research Articles

Transition to turbulence in hypersonic flow over a compression ramp due to upstream forcing

Several transition scenarios are present in a hypersonic compression-ramp flow. In our previous work (Cao et al., J. Fluid Mech., vol. 941, 2022, p. A8), a complete transition process induced by the global instability of a compression-ramp flow was revealed. In a globally stable flow, however, the transition to turbulence can be promoted by convective instabilities, which is the focus of this work. The same flow conditions as in our previous work (Mach number 7.7, Reynolds number $8.6\times 10^5$ based on the flat-plate length) are considered here. Owing to a smaller ramp angle, a weakly separated flow forms on the compression ramp, which supports no global instability. Resolvent analysis identifies low-frequency streamwise streaks as the optimal response of base flow to upstream forcing. Local stability analysis reveals Mack's second mode in the boundary layer downstream of reattachment. By introducing random disturbances upstream of separation in direct numerical simulations, we observe breakdown to turbulence downstream of reattachment. Two transition scenarios are revealed, and they are highly dependent on the amplitude of upstream disturbances. For a large amplitude, strong streamwise streaks develop near the reattachment region, which break down to turbulence quickly. However, when the disturbance amplitude is reduced, the second-mode instability dominates the transition to turbulence.

Bi-global stability of supersonic backward-facing step flow

Supersonic backward-facing step (BFS) flow is numerically studied using direct numerical simulation (DNS) and global stability analysis (GSA) with a free stream Mach number of 2.16 and a Reynolds number of 7.938 × 105 based on the flat-plate length L and free stream conditions. Two-dimensional BFS flow becomes unstable to three-dimensional perturbations as the step height h exceeds a certain value, while no two-dimensionally unstable mode is found. Global instability occurs with the fragmentation of the primary separation vortex downstream of the step. Two stationary modes and one oscillatory unstable mode are obtained at a supercritical ratio of L/h = 32.14, among which the two stationary modes originate from the coalescence of a pair of conjugate modes. The most unstable mode manifests itself as streamwise streaks in the reattached boundary layer, which is similar to that in shock-induced separated flow, although the flow separation mechanisms are different. Without introducing any external disturbances, the DNS captures the preferred perturbations and produces a growth rate in agreement with the GSA prediction in the linear growth stage. In the quasi-steady stage, the secondary separation vortex breaks up into several small bubbles, and the number of streamwise streaks is doubled. A low-frequency unsteadiness that may be associated with the oscillatory mode is also present.

Critical heat flux and bubble behaviour study on differently oriented flat plates during pool boiling

An experimental study is brought off to analyse the effect of flat plate length, width, orientation, and pool liquid temperature on CHF under atmospheric conditions during pool boiling. The bubble nucleation and departure for the aforementioned parametric and operational conditions are discussed. Based on bubble behavior, various pool boiling regimes under uniform heat flux conditions are investigated. The pool is maintained at 25℃ and saturation temperature corresponding to ambient pressure. The occurrence of burnout on the heater plates is analysed on the basis of bubble behaviour. It is analysed that prior to the occurrence of CHF a liquid film enclosed with vapour leads to initiate the dry patch. It is observed that with an increase in pool temperature, the magnitude of CHF reduces. It has been estimated that there is a decrement of around 62 % in the magnitude of CHF in saturated conditions as compared with subcooled conditions. The vertical orientation of the plates results in a higher CHF magnitude. In the subcooled pool, the CHF in vertical orientation ranges between 6.197 MW/m2 to 2.909 MW/m2. Whereas in the saturated pool the CHF magnitude in vertical orientation ranges between 2.652 MW/m2 to 0.998 MW/m2. As the length of the heater plate increases, the CHF value reduces. The minimum magnitude of CHF is obtained as 0.898 MW/m2 for downward facing heater of 300 mm in length at the saturated pool. Higher the width lesser the CHF. The obtained experimental results are compared with available correlations to access its viability. An empirical correlation is suggested, implicating the effect of heater length, width, orientation, and pool temperature for the pool boiling CHF on flat plates.

Control of supersonic compression corner flow using a plasma actuator

The control performance of a pulsed nanosecond dielectric barrier discharge (NSDBD) plasma actuator with varying pulse voltages and locations on a supersonic compression corner is studied using experiments and numerical simulations. The compression corner with a flat plate length of 60 mm and a ramp angle of 10° under laminar flow separation is experimentally investigated in a Ludwieg wind tunnel under a unit Reynolds number of 7.8 × 106 m−1 and Mach number of 4. The plasma actuators are placed either upstream or downstream of the separation point, extending in the spanwise direction. The Schlieren technique is used to visualize the shock wave interaction and estimate the propagation speed of the induced shock by the plasma actuator. For the numerical simulations, a one-zone inhomogeneous phenomenological plasma model is adopted to predict key discharge parameters and simulate the fast-heating region. The results show that the reduction of separation bubble length is up to 17% and 45%, respectively, in the cases of upstream and downstream of the separation point under a high applied voltage of 50 kV. The evolution of the flow structures is examined to reveal the underlying control mechanism. The results indicate that the high-speed external fluid is entrained into the original separation region after NSDBD activation upstream of the separation point, resulting in flow reattachment upstream of the corner. The entrained fluid with high momentum compels the main separation to move downstream, accompanied by the fragmentation of the original shear layer. Furthermore, the suppression of the separation region is more effective when the plasma actuator is installed close to the separation region and in the first 200 μs during one pulse, providing a good suggestion for the actuation frequency and installed location.

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

In this work, a transition process in a hypersonic flow over a cold-wall compression ramp is studied using direct numerical simulation (DNS) and global stability analysis (GSA). The free-stream Mach number and the Reynolds number based on the flat-plate length are 7.7 and $8.6 \times 10^5$ , respectively. The shock-induced pressure rise causes the boundary layer to separate on the flat plate, forming a separation bubble around the corner. Without introducing any external disturbances, the DNS captures the transition to turbulence downstream of flow reattachment. The DNS results agree well with the experimental data as well as theoretical predictions. To uncover the intrinsic instability in the flow system, GSA is employed to investigate the three-dimensionality of the two-dimensional base flow. Several stationary and oscillatory unstable modes are revealed, which result in spanwise periodicity inside and downstream of the separation bubble. The GSA and DNS results indicate that the intrinsic instability of the flow system triggers the formation of streamwise counter-rotating vortices and boundary-layer streaks near reattachment. The downstream transition to turbulence starts from the breakdown of the streamwise vortices and streaks. Moreover, the second harmonic of the most unstable global mode and a broadband low-frequency unsteadiness occur in the saturated flow, which has a significant influence on the transition process. In summary, the present study demonstrates a transition process in a hypersonic compression-ramp flow as a result of the intrinsic instability of the flow system.

Unsteady effects in a hypersonic compression ramp flow with laminar separation

Abstract

Effect of Görtler-like vortices of various intensity on heat transfer in supersonic compression corner flows

Experiments on heat transfer over Mach 8, 15° compression corner flow affected by Görtler-like reattachment vortices of controllable intensity are carried out in the shock wind tunnel UT-1 M (TsAGI). Experiments cover two Reynolds numbers Re∞,L=(1.75±0.08) × 105 and Re∞,L=(3.90±0.15) × 105 based on the sharp flat plate length at which the reattachment flow is close to laminar or beginning transitional, respectively. The effect of streamwise vortices of different intensity on spanwise variations of the heat flux and its spanwise-averaged level at the reattachment region is investigated. The intensity of the vortices is varied by accurate controlling the height of a spanwise rake of cylindrical pins (seeding elements) placed on the plate ahead of the separation bubble.

Cyclic performance analysis of a high temperature flat plate thermal energy storage unit with phase change material

The cyclic performance of a high temperature flat plate thermal energy storage (FPTES) with phase change material (PCM) is numerically studied. Based on a one-dimensional model, both the thermal conduction and phase change within the PCM plate in the direction normal to the flow direction of heat transfer fluid (HTF) are taken into consideration in the this study. The proposed model is validated against the reported results and the numerical results calculated by a commercial CFD software. Then, the proposed model is used to simulate the cyclic charging and discharging processes of the FPTES with PCM. In addition, the influence of the cut-off values, HTF mass flow rate, and flat plate length and thickness on the charging efficiency and capacity ratio are investigated. The results show that the charging and discharging processes reach a repeatable state after several cycles, and the repeatable cycle is very different from the first cycle. The capacity ratio and the charging/discharging time increase with the cut-off values. An optimum charging cut-off value exists to achieve the highest charging efficiency. Extending the flat plate length helps to increase the capacity ratio and charging efficiency. Besides, the decreases in HTF mass flow rate and plate thickness can increase the charging efficiency and capacity ratio. Finally, a system design guideline of the FPTES with PCM is proposed based on the developed model and the gained results.

Pressure Gradient Effects on Smooth- and Rough-Surface Turbulent Boundary Layers—Part II: Adverse Pressure Gradient

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

Grid-point requirements for large eddy simulation: Chapman’s estimates revisited

Resolution requirements for large eddy simulation (LES), estimated by Chapman [AIAA J. 17, 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. The new estimates indicate that the number of grid points (N) required for wall-modeled LES is proportional to ReLx, but a wall-resolving LES requires ÑReLx13/7, where Lx is the flat-plate length in the streamwise direction. On the other hand, direct numerical simulation, resolving the Kolmogorov length scale, requires ÑReLx37/14.

Hypersonic Inlet Studies for a Small Scale Rocket-Based Combined-Cycle Engine

Experimental tests on a small-scale rocket-based combined-cycle model engine at Mach 8 were conducted to investigate the influence of inlet airflow changes on the engine performance. Flat plates of different lengths with a sharp leading edge and parallel to the freestream airflow, simulating the presence of vehicle body, were mounted before the inlet bottom surface. The test results indicated that fuel ignition, combustion chamber pressure, and engine net thrust were strongly affected by moderate changes of the flat plate length. The formation of an oblique shock wave due to hypersonic viscous interaction effects was observed above the flat plates. External compression of the captured airflow and lateral mass spillage were quantified on the basis of wall pressure measurements near the engine inlet for all tested plates. A convenient flat plate length range was identified that minimized spillage and optimized the engine performance.

Kinetic Model Solution for Microscale Gas Flows

A kinetic theory analysis is made of low-speed gas flows around microscale flat plates. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation together with the discrete ordinate method. The advantage of the present method is that it does not suffer from statistical noise, which is common in particle-based methods. Calculations are made for flows around a flat plate with zero thickness and a5 %flat plate. Results for the 5% flat plate at a freestream Mach number 0.5 showed good agreement with those from the direct simulation Monte Carlo method. It is shown that strong rarefaction effects exist around the leading and trailing edges. Results from the present method at a freestream Mach number 0.087 also showed similar nonequilibrium effects. Comparison of results with those from the information preservation method and numerical solutions of the Navier‐Stokes equations showed some differences in details near the leading and trailing edges. Nomenclature Ac = collision frequency d = characteristic length of the flowfield F = Maxwell‐Boltzmann distribution f = distribution function g, h = reduced distribution functions Kn = Knudsen number L = length of flat plate l = normal distance from plate surface R =g as constant t = thickness of flat plate U∞ = free stream velocity Vx =v elocity of molecule in the x direction Vy =v elocity of molecule in the y direction Vz =v elocity of molecule in the z direction λ = mean free path I. Introduction

Viscous interaction phenomena in hypersonic wedge flow

We deal with an experimental investigation carried out to study some aspects of shock/boundary-layer interaction in nominally two-dimensional hypersonic wedge flow, i.e., over flat plate/rump configurations. These flow conditions are two dimensional only geometrically because some spanwise periodic variations of the heat flux over the ramp in the reattaching flow region are observed. The measurements, basically made by means of a computerized infrared (IR) imaging system, have been performed in a blowdown wind tunnel at Mach number equal to 7.14 and unit Reynolds number ranging from 7.6 x 10 6 to 24 X 10 6 /m. The influence of the leading-edge shape (bluntness and geometry), flat plate length, and ramp angle on the separation region, average heat transfer at reattachment, and wavelength of the heat transfer variations has been analyzed. IR results are compared to other experimental data as well as to semiempirical correlations for the heat flux peak.

Viscous and Thermal Wakes in MHD Generators

SEPARATE analytical studies of the development of velocity and thermal wakes in MHD generators are conducted and their influence on the performance of the generator is evaluated. l Such wakes could be the result of inlet vanes in a linear generator to reduce end losses or inlet swirl vanes in a disk generator to improve efficiency. Nomenclature £ = length of flat plate u - fluid velocity in x-direction €0 = virtual kinematic viscosity r) = similarity coordinate for wake

Boundary layer along the initial length of a flat plate at zero incidence with homogeneous suction

An investigation has been made into the two-dimensional laminar incompressible boundary layer along the initial length of a semi-infinite flat plate at zero incidence with homogeneous suction. The momentum and the kinetic energy integral equations have been numerically integrated with the aid of a singly infinite system of boundary layer velocity profiles.