Data Reduction And Error Analysis For The Physical Sciences

Free underexpanded jets in a quiescent medium: A review

Control of flow-induced forces on a circular cylinder using a detached splitter plate is numerically studied for laminar flow. A splitter plate with the same length as the cylinder diameter is placed horizontally in the wake region. Suppressing the vortex shedding, the plate significantly reduces drag force and lift fluctuation; there exists an optimal location of the plate for maximum reduction. However, they sharply increase as the plate is placed further downstream of the optimal location. This trend is consistent with the experimental observation currently available in the case of turbulent wake.

Reduction of flow-induced forces on a circular cylinder using a detached splitter plate

Recent advances in the aerothermodynamics of spiked hypersonic vehicles

Numerical investigation on the shock wave transition in a three-dimensional scramjet isolator

Preface. About the Author. 1 Basic Facts. 1.1 Definition of Gas Dynamics. 1.2 Introduction. 1.3 Compressibility. 1.4 Supersonic Flow What is it? 1.5 Speed of Sound. 1.6 Temperature Rise. 1.7 Mach Angle. 1.8 Thermodynamics of Fluid Flow. 1.9 First Law of Thermodynamics (Energy Equation). 1.10 The Second Law of Thermodynamics (Entropy Equation). 1.11 Thermal and Calorical Properties. 1.12 The Perfect Gas. 1.13 Wave Propagation. 1.14 Velocity of Sound. 1.15 Subsonic and Supersonic Flows. 1.16 Similarity Parameters. 1.17 Continuum Hypothesis. 1.18 Compressible Flow Regimes. 1.19 Summary. Exercise Problems. 2 Steady One-Dimensional Flow. 2.1 Introduction. 2.2 Fundamental Equations. 2.3 Discharge from a Reservoir. 2.4 Streamtube Area Velocity Relation. 2.5 de Laval Nozzle. 2.6 Supersonic Flow Generation. 2.7 Performance of Actual Nozzles. 2.8 Diffusers. 2.9 Dynamic Head Measurement in Compressible Flow. 2.10 Pressure Coefficient. 2.11 Summary. Exercise Problems. 3 Normal Shock Waves. 3.1 Introduction. 3.2 Equations of Motion for a Normal Shock Wave. 3.3 The Normal Shock Relations for a Perfect Gas. 3.4 Change of Stagnation or Total Pressure Across a Shock. 3.5 Hugoniot Equation. 3.6 The Propagating Shock Wave. 3.7 Reflected Shock Wave. 3.8 Centered Expansion Wave. 3.9 Shock Tube. 3.10 Summary. Exercise Problems. 4 Oblique Shock and ExpansionWaves. 4.1 Introduction. 4.2 Oblique Shock Relations. 4.3 Relation between and . 4.4 Shock Polar. 4.5 Supersonic Flow Over a Wedge. 4.6 Weak Oblique Shocks. 4.7 Supersonic Compression. 4.8 Supersonic Expansion by Turning. 4.9 The Prandtl Meyer Expansion. 4.10 Simple and Nonsimple Regions. 4.11 Reflection and Intersection of Shocks and Expansion Waves. 4.12 Detached Shocks. 4.13 Mach Reflection. 4.14 Shock-Expansion Theory. 4.15 Thin Aerofoil Theory. 4.15.1 Application of Thin Aerofoil Theory. 4.16 Summary. Exercise Problems. 5 Compressible Flow Equations. 5.1 Introduction. 5.2 Crocco's Theorem. 5.3 General Potential Equation for Three-Dimensional Flow. 5.4 Linearization of the Potential Equation. 5.5 Potential Equation for Bodies of Revolution. 5.6 Boundary Conditions. 5.7 Pressure Coefficient. 5.8 Summary. Exercise Problems. 6 Similarity Rule. 6.1 Introduction. 6.2 Two-Dimensional Flow: The Prandtl-Glauert Rule for Subsonic Flow. 6.3 Prandtl Glauert Rule for Supersonic Flow: Versions I and II. 6.4 The von Karman Rule for Transonic Flow. 6.5 Hypersonic Similarity. 6.6 Three-Dimensional Flow: Gothert s Rule. 6.7 Summary. Exercise Problems. 7 Two-Dimensional Compressible Flows. 7.1 Introduction. 7.2 General Linear Solution for Supersonic Flow. 7.3 Flow Over a Wave-Shaped Wall. 7.4 Summary. Exercise Problems. 8 Flow with Friction and Heat Transfer. 8.1 Introduction. 8.2 Flow in Constant Area Duct with Friction. 8.4 Flow with Heating or Cooling in Ducts. 8.5 Summary. Exercise Problems. 9 Method of Characteristics. 9.1 Introduction. 9.2 The Concepts of Characteristic. 9.3 The Compatibility Relation. 9.4 The Numerical Computational Method. 9.5 Theorems for Two-Dimensional Flow. 9.6 Numerical Computation with Weak Finite Waves. 9.7 Design of Supersonic Nozzle. 9.8 Summary. 10 Measurements in Compressible Flow. 10.1 Introduction. 10.2 Pressure Measurements. 10.3 Temperature Measurements. 10.4 Velocity and Direction. 10.5 Density Problems. 10.6 Compressible Flow Visualization. 10.7 Interferometer. 10.8 Schlieren System. 10.9 Shadowgraph. 10.10 Wind Tunnels. 10.11 Hypersonic Tunnels. 10.12 Instrumentation and Calibration of Wind Tunnels. 10.13 Calibration and Use of Hypersonic Tunnels. 10.14 Flow Visualization. 10.15 Summary. Exercise Problems. 11 Ramjet. 11.1 Introduction. 11.2 The Ideal Ramjet. 11.3 Aerodynamic Losses. 11.4 Aerothermodynamics of Engine Components. 11.5 Flow Through Inlets. 11.6 Performance of Actual Intakes. 11.7 Shock Boundary Layer Interaction. 11.8 Oblique Shock Wave Incident on Flat Plate. 11.9 Normal Shocks in Ducts. 11.10 External Supersonic Compression. 11.11 Two-Shock Intakes. 11.12 Multi-Shock Intakes. 11.13 Isentropic Compression. 11.14 Limits of External Compression. 11.15 External Shock Attachment. 11.16 Internal Shock Attachment. 11.17 Pressure Loss. 11.18 Supersonic Combustion. 11.19 Summary. 12 Jets. 12.1 Introduction. 12.2 Mathematical Treatment of Jet Profiles. 12.3 Theory of Turbulent Jets. 12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis. 12.5 Expansion Levels of Jets. 12.6 Control of Jets. 12.7 Summary. Appendix. References. Index.

Applied Gas Dynamics

An experimental investigation was carried out to study the 
effectiveness of micro-jets to control base pressure in suddenly
expanded axi-symmetric ducts. Four micro-jets of 1 mm orifice diameter 
located at 90$^\circ$ interval along a pitch circle diameter of 1.3 
times the nozzle exit diameter in the base region was
 employed as active controls. The Mach numbers of the suddenly 
expanded flows were studies 2.0, 2.5 and 3.0. The jets were expanded 
suddenly 
into an axi-symmetric tube with cross-sectional area 2.56, 3.24, 4.84, 
and 6.25 times that of nozzle exit diameter. The length-to-diameter 
ratio of the sudden expansion tube was varied from 10 to 1. The jets 
were operated at an over expansion level of Pe/Pa = 0.277. 
The wall pressure distribution in the suddenly enlarged duct was also
measured. It is found that the micro-jets can serve as active 
controllers for
base pressure. Also, the wall pressure distribution is not adversely 
influenced by the micro-jets. From the present investigation it is 
evident that for a given Mach number and nozzle pressure ratio one can 
identify the enlargement length to diameter ratio which will result 
in maximum increase/decrease of base pressure.

Active Control of Suddenly Expanded Flows from Overexpanded Nozzles

A spike attached to a hemispherical body drastically changes its flowfield and influences aerodynamic drag in a hypersonic flow. It is, therefore, a potential candidate for drag reduction of a future high-speed vehicle. The effect of the spike length, shape, spike nose configuration and angle-of-attack on the reduction of the drag is experimentally studied with use of hypersonic wind-tunnel at Mach 6. The effects of geometrical parameters of the spike and angle-of-attack on the aerodynamic coefficient are analysed using schlieren picture and measuring aerodynamic forces. These experiments show that the aerodisk is superior to the aerospike. The aerodisk of appropriate length, diameter and nose configuration may have the capability for the drag reduction. The inclusion of an aero disk at the leading edge of the spike has an advantage for the drag reduction mechanism if it is at an angle-of-attack, however consideration to be given for increased moment resulting from the spike is required.

Experimental investigation on spiked body in hypersonic flow

The results of an experimental investigation carried out to
control the base pressure in a suddenly expanded axi-symmetric passage are presented in this paper. Active control in the form of micro-jets was employed to control the base pressure. Air injection at four locations at the base, symmetric to the nozzle axis was used as the
active control. The jet Mach numbers at the entry to the suddenly expanded duct, studied were 1.87, 2.2 and 2.58. The length-to-diameter ratio of the suddenly expanded duct was varied from 10 to 1. Nozzles generating the above jet Mach numbers were operated with nozzle pressure ratio (NPR) in the range 3 to 11. In addition to base pressure, wall pressure field along the enlarged duct length was also
studied. It is found that the active control in the form of blowing through small orifices (micro-jets) are effective in controlling the base pressure field. As high as 95 per cent increase in base pressure was achieved for certain combination of parameters of the present study. From the present investigation it is evident that for a given
Mach number and NPR one can identify the L/D which will result in maximum increase/decrease of base pressure.

Control of Suddenly Expanded Flows with Micro-Jets

Experiments were carried out to study the effect of the tabs with limiting length, termed Rathakrishnan limit, on controlling the mixing and acoustic characteristics of free jets. The limiting tab is found to be efficient in promoting the jet mixing even in the presence of an adverse pressure gradient. Furthermore, the limiting tab is found to bemost efficient in promoting the mixing near the correct expansion rather than at an underexpanded condition, with a favorable pressure gradient at the nozzle exit. The reason behind theworking of the limiting tab in the formof a cross wire is discussed forMach 1.6, 1.79, and 2.0 jets. As high as 50%reduction in the core length is achieved using a cross wire forMach 1.79 jet operatedwith nozzle pressure ratio 5.66. The combination of thewaves in the jet core and their interaction with the detached shock envelop generated by the wire has a strong influence on the overall jet noise and its spectral content. Even though thewire reduced the overall noise of the jet and the reduction is significant formany cases of the present study, it caused an increase of screech amplitude for some cases. Jet noise reduction was found to be sensitive to the wire orientation.

Ethirajan Rathakrishnan

Papers

Applied Gas Dynamics

Active Control of Suddenly Expanded Flows from Overexpanded Nozzles

Experimental investigation on spiked body in hypersonic flow

Control of Suddenly Expanded Flows with Micro-Jets

Experimental Studies on the Limiting Tab