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The surface heat flux on a 100 mm diameter hypersonic sphere was reduced through surface roughness on its forebody. The test model was subjected to a hypersonic freestream of Mach 8.8 and Reynolds number 1.98 million/m, in a shock tunnel. Forebody surface heat transfer rates measured on smooth and rough spheres, under the same free-stream conditions, were compared. The comparison of heat flux indicated an overall reduction in surface heating rates on the rough model, which could be attributed to the delayed nose tip transition. The surface roughness on the forebody of the model generated miniature cavities. Stability of the free shear layer over the miniature cavities and entrapment of the destabilizing vortices in the cavities, make the flow over the rough test model more stable than the attached boundary layer over the smooth model, under transitional conditions.

Hypersonic reentry vehicles have large forebody bluntness to shield from high aerodynamic heating. The large bluntness at hypersonic Mach numbers generates strong bow shock waves due to which the shock layers will have strong entropy layers, which are a region of strong vorticity [

A patch of large roughness, which is of the order of boundary layer thickness on a surface can give rise to a cavity effect, which when subjected to a moderate flow speed can delay transition by virtue of vortex entrapment and persistence in the cavities [

Reentry vehicles require Thermal Protection Systems (TPS) in addition to a natural heat shield like forebody bluntness, to withstand aerodynamic heating. The thermal protection systems can be classified as active, passive and ablative depending upon their mode of function [

The present study had an objective of investigating the effect of such a surface roughness on the aerothermodynamics of the vehicle. After completing similar investigations on a large angled blunt cone [

The experiments were performed in the IIT Bombay Shock Tunnel (IITB-ST) [_{0}), and the time-history of the total pressure ratio (P_{02}/P_{0}) at the test location are presented in _{0} pressure trace indicates the available test time, while the useful test time is indicated by the stable region of the P_{02}/P_{0 }trace.

The test model was a sphere of 100 mm diameter as shown in

Mach no. | P_{∞} (Pa) | T_{∞} (K) | H_{0} (MJ/kg) | Re/m (×10^{6}) |
---|---|---|---|---|

8.8 ± 0.2 | 112 ± 5 | 65 ± 2 | 1.12 ± 0.4 | 1.98 ± 0.02 |

and an effective thermal product range of 5857 - 12,306 Jm^{−2}∙K^{−1}∙s^{−1/2}. The thermocouples were instrumented with INA128 instrumentation amplifiers with a gain factor of 500 and a peak operating frequency of 40 kHz. In the rough surface, the sensing junctions of the thermocouples were at half the roughness height from the model surface. The sensor placement in the rough model is presented in

The shock tunnel is equipped with an 8-inch Z-type Schlieren system [

The output of the sensors in the test model was acquired on a data acquisition system, equipped with NI-PCI-6115 S series data cards (National Instruments Corporation, USA), at a sampling rate of 1 MS/s. The acquired signals were post-processed using a 4^{th} order IIR low-pass filter (cut-off frequency of 10 kHz) to eliminate the high-frequency spurious noise.

The surface heat-flux was reduced from the acquired temperature-time history signals of the flush mounted thermocouples based on the methodology proposed

by Cook & Felderman, which is on the assumption of 1-D heat conduction in a semi-infinite slab [

Q ( t ) = β π α [ E ( t ) t + 1 2 ∫ 0 t E ( t ) − E ( τ ) ( t − τ ) 3 / 2 d τ ] (1)

Equation (1) was numerically processed using a piece-wise linear function for E(τ), as expressed in Equation (2).

E ( τ ) = E ( t i − 1 ) + E ( t i ) − E ( t i − 1 ) Δ t ( τ − t i − 1 ) (2)

where, t i − 1 ≤ τ ≤ t i and i = 1, 2, 3, ⋯ , n. The Equation (2) was substituted into Equation (1) and was integrated to obtain the following expression:

Q ( t ) = β π α [ E ( t n ) t n + ∑ i = 1 n − 1 { E ( t n ) − E ( t i ) t n − t i − E ( t n ) − E ( t i − 1 ) t n − t i − 1 + 2 E ( t i ) − E ( t i − 1 ) t n − t i + t n − t i − 1 } + E ( t n ) − E ( t n − 1 ) Δ t ] (3)

Equation (3) was programmed to obtain the heat flux-time histories from the temperature-time histories of the thermocouples. The heat flux signals were time-averaged over the useful test time of the shock tunnel for reading.

^{2} for the

smooth and the rough models, respectively. The measured heat-flux distribution over the smooth sphere indicated a transitional trend as seen in the plot in

The large-scale roughness generated a multiple-cavity effect on the forebody of the sphere. Under moderate velocities, such as in zone-2, the roughness cavities could engulf the destabilizing entropy layer in the form of trapped large eddies thereby damping the associated instabilities. The destabilizing factor of the entropy layer was isolated, damped and confined to these cavities till the vortices started shedding, and the separated shear layer over the cavities was more stable than its transitional, attached counterpart [

The results presented in

Effect of surface roughness on wall heating rates of a 100 mm diameter sphere was investigated in a hypersonic freestream of Mach 8.8. The roughness on the forebody of the sphere was found to reduce surface heat flux in a zone with moderate flow velocity. The reason could be attributed to vortex persistence in the roughness cavities and delayed-transition. Qualitative flow visualization on the models corroborated the measured heat flux data. The study has relevance to ablative Thermal Protection Systems (TPS) of reentry capsules.

This work was funded by the ISRO-IITB-Space Technology Cell, IIT Bombay (Grant# 15ISROC010).

Irimpan, K.J., Menezes, V., Srinivasan, K. and Hosseini, H. (2018) Nose-Tip Transition Control by Surface Roughness on a Hypersonic Sphere. Journal of Flow Control, Measurement & Visualization, 6, 125-135. https://doi.org/10.4236/jfcmv.2018.63011

E(t): time dependent voltage

H_{0}: total enthalpy

P_{0}: reservoir pressure

P_{02}: pitot pressure

P_{∞}: static pressure

Q(t) : unsteady heat flux

R_{b}: base radius

Re: Reynolds number

S: wetted length

T_{∞}: static temperature

t: time

w.r.t.: with respect to

α: thermocouple sensitivity

β: effective thermal product

τ: time variable