These are the two techniques commonly used to estimate the surface heat flux in the above applications. These computational studies demonstrate the effect of large simulation duration on heat flux prediction due to the transient and multidimensionality of heat transfer.
INTRODUCTION
History of the Flight
These techniques are used to avoid the heat of the vehicle and are therefore called passive cooling techniques. The literature describes the heat transfer analysis of hypersonic flows based on both analytical and numerical approaches.
Literature Review on Analytical Heat Transfer Studies
Comparison of the obtained heat transfer coefficients with the existing results was found with reasonable accuracy. Alifanov and Golub (2003) derived the solution of the transient heat conduction equation of two axially bounded heterogeneous cylinders.
Literature Review on Numerical Heat Transfer Studies
Wang (2000) investigated three-dimensional conjugate heat transfer analyzes for the manifold located upstream of the ramjet fuel injector. Nikas and Panagiotou (2013) investigated a numerical simulation of the conjugate heat transfer effects within a computer chassis cooled by fans forcing heat convection.
Motivation for PhD Work
Conjugate heat transfer analysis has been regularly used by various researchers in subsonic or incompressible flow situations. With this in mind, an explanatory simulation for hypersonic flow over a flat plate of finite thickness can demonstrate an attempt to measure heat transfer.
Objective of the Thesis
Organization of the Thesis
PREDICTION OF TRANSIENT HEAT FLUX USING VARIOUS
Preface
Current studies are planned to apply a new heat flux retrieval technique and to evaluate the effectiveness of widely used techniques to retrieve the heat flux from the temperature data. Temperature signals obtained from the CFD simulations, ground-based experimental testing and flight testing are used to evaluate the performance of a specific technique to predict the heat flux.
Computational Technique for Surface Temperature Prediction
- Surface temperature and heat flux histories for standard cases
The present finite volume based solver carries the capability of composite heat conduction with heat flux continuum and interface temperature uniqueness. In the case of a linear heat load (Fig. 2.4-a), the rate of temperature rise is seen to be dependent on the rate of change of the applied heat flux.
One-Dimensional Heat Conduction Modeling
- Temperature discretization and heat flux predictions
- Laplace technique for heat flux prediction
- Surface temperature and heat flux histories for standard cases
- Surface temperature and heat flux histories for experimental cases
The temperature time histories along with the surface material properties (Macor) are used with temperature as a boundary condition for surface heat flux prediction. Regarding the prediction duration of 20 ms, all the temperature and surface heat flux signals appear to be in good agreement. All techniques discussed are considered to recover the surface heat flux in both cases (Figs. 2.8-a and 2.8-b).
All of the methods discussed above are implemented here for retrieving surface heat flux history and are presented in Figs. Based on the results presented above, one can infer that discretization of temperature data plays a crucial role in recovering surface heat flux.
Summary
Preface
Governing Equations for Fluid Flow
DEVELOPMENT OF SOLVERS FOR FLUID FLOW AND SOLID MIXING. is the specific enthalpy given by p h e. ρ , qx and qyheat flux in the x and y direction, respectively. The above governing equations are reduced to non-dimensional form using free-flow variables and the characteristic dimension of the object leading to tracking the non-dimensional variables. Here we are assuming x, y, u..etc as non-dimensional variables and x*, y*, u*..etc are the dimensional variables for simplicity.
In the above equations Re∞ is the free-stream Reynolds number, Pr∞ is the Prandtl number, and M∞ is the free-stream Mach number. Since the numbers of unknowns are more than the number of equations, the closure problem is solved using an additional equation which is nothing but the nondimensional form of the equation of state given by, . where , R nondimensional gas constant.
Finite Volume Method (FVM)
Here U = A1 ∫∫UdA (Average value of U over the entire volume) The current is given by F =FI−FV.
Discretisation Schemes for Flux calculation
Advection Mach number is evaluated as the sum of the left and right divided Mach number. Second term in the above equation has dissipative character, which is scaled by the scalar value (Mn)I+1 2. When advection Mach number (Mn)I+1 2 tends to zero, the dissipation term in Eq.3.18 approaches zero.
To maintain the accuracy of the boundary layer scheme, the parameter δ in the normal direction of the wall could be reduced.
Discretization of Viscous Fluxes
Fluid Flow Boundary Conditions
Governing Equations for Solid Domain Conduction Solver
Boundary Conditions for Solid Domain Conduction Solver
Results and Discussion
- Test Case 1: Hypersonic flow over an isothermal flat plate
- Test Case 2: Transient heat conduction in a slab
- Test Case 3: Transient heat conduction through a composite slab
Here the skin friction (Cf ) and the Stanton number decrease along the length of the plate. This agreement between different wall parameters, in local magnitude and global variation, confirms the accuracy of the present solver. Furthermore, analytical formulation for the temperature variation along the plate depth in a particular case is given as [Holman (1989)].
Therefore, the chosen test case of transient heat conduction in a plate of finite thickness is found to be effective in confirming the spatial and temporal accuracy of the internal conduction solver. Encouraging agreement with such physical expectations and with results reported in the literature confirms the accuracy of the wire resolver.
Summary
COUPLING TECHNIQUES FOR THE CONJUGATE HEAT
- Preface
- Computational Methodology for CHT studies
- Hypersonic Flow Over Flat Plate
- Summary
However, when the calculations in the fluid and solid domains are performed simultaneously using interface boundary conditions as shown in Fig. Here, the time marching of the solid domain should be performed using the time step obtained from the fluid domain. The maximum temperature in the solid domain is noted at this step and calculations in the liquid domain are completed.
Achieving this criterion reinitiates simultaneous computations of the solid and fluid domain using common time step obtained from the fluid domain. Residual of the fluid flow solver and maximum temperature in solid domain are flags used for coupling and uncoupling of solid and fluid domain calculations.
CONJUGATE HEAT TRANSFER STUDY IN HYPERSONIC FLOW
Preface
Simulations are also run on the same configuration for a longer duration of 0.1 ms to understand the effect of wall heating on the fluid domain. The central theme of this chapter is the simulation of heat transfer measurement experiments using the conjugate heat transfer methodology. Joint and separate CHT techniques are used to demonstrate this topic for hypersonic flow over a flat plate of finite thickness.
The effect of variation in wall properties on fluid flow has also been investigated on a relatively large time scale (~0.1s) using loosely coupled CHT technique. The thicknesses of the thermal boundary layer and the velocity boundary layer are used to understand the interaction between wall heating and hydrodynamic boundary layer.
Computational Methodology for CHT studies
- CHT simulation for short time scale applications (shock tunnel)
- CHT simulation for large time scale applications
The temporal variation of heat flux at these locations of the plate is also shown in fig. Streamwise increase in velocity boundary layer and thermal boundary layer thicknesses are evident in both cases. Quantitative variation of thermal and velocity boundary layer thicknesses along the length of at the end of the simulation (0.1 s) is plotted in Fig.
As noted earlier, the increase in velocity boundary layer thickness downstream of the leading edge is also evident from Figs. As a result, the thickness of the thermal boundary layer at different places in the direction of the flow is shown in Fig.
Summary
Preface
Increases in wall temperature and decreases in surface heat flux have been noted using strong and loose coupling techniques as simulation time increases. Efforts are also made to justify the difference in stagnation point heat flux prediction using conventional computational and experimental analysis.
Computational Strategy for Finite Thickness of Cylinder
Decoupled fluid and solid domain analysis is found to be useful for typical shock tunnel test durations (~1 ms), while loose-coupling technique studies are advisable for timescales equivalent to flight testing (~1 s). Adiabatic wall heat flux is considered zero. Isothermal wall temperature is considered constant (T=const) Exhaust Supersonic exhaust limit.
Results and Discussion
The temperature history and time trace of the wall heat flux at the stagnation point for the simulation duration of 10 ms are shown in Fig.6.7 and Fig. The underprediction of heat flux at the stagnation point using tight and loose coupling techniques can be justified by the solid domain temperature contours shown in Fig. The distribution of heat flux at the wall obtained from all techniques is compared with the results reported in the literature (Fig. 6.10).
The predictions of time trace of stagnation point temperature and heat flux are shown in Fig. For simulation time of 1s, the maximum discrimination at the stagnation point is seen for LC-CHT method where the heat flux is underpredicted by 65% compared to DC-CHT technique.
Summary
CONJUGATE HEAT TRANSFER ANALYSIS FOR COMPOSITE
- Preface
- Computational Strategy
- Results and Discussion
- Fluid flow study with isothermal and adiabatic boundary
- CHT analysis for flow over a composite flat plate
- CHT analysis for flow over a composite cylinder
- Summary
The effect on the temperature variation at the surface of the solid is also currently of interest. There is also a sudden change in temperature at the solid-solid interface in CHT simulation and fluid flow solver (N-S solver). In both cases for flat plates of finite thickness, the maximum temperature increase in the solid domain is noticed on the Macor side.
Here, as expected, a slightly higher temperature rise is observed for the Macor material at the leading edge compared to the aluminum at the leading edge. Whereas in the opposite case (case II), although there is an isothermal boundary at the location, the temperature rise is higher.
CONJUGATE HEAT TRANSFER ANALYSIS OF HYPERSONIC
- Preface
- Computational Strategy for Double Wedge
- Results and Discussion
- Summary
Accordingly, surface pressure variation is plotted in the Fig. Excellent agreement of the wall pressure trace with the present simulations can be experienced from this figure. For a better understanding of the interaction, surface heat flux variation along the length of the double wedge is plotted in Fig. In the case of isothermal wall condition, local heat transfer gradually decreases downstream in the first wedge due to the spatial development of the boundary layer.
Surface temperature along the length of the double wedge of adiabatic wall is shown in Fig. Such variation in skin friction coefficient along the length of the double wedge crosses the zero line close to the corner of the double wedge geometry.
CONCLUSIONS AND FUTURE WORK
Conclusion
Coupled and decoupled CHT solvers are used for short and long duration transient temperatures and surface heat flux. In addition, the effect of the simulation time on the heat flux and fluid flow properties of the interface is analyzed. Moving along the surface of the cylinder from the stagnation point to the 90 degree current deflection angle, the difference in surface heat flux is reduced to 35%.
This study mainly focuses on the variation of separation bubble length, skin friction coefficient and heat flux caused by the variation in heating rates of walls with different wall materials and time scales. When using Macor and thermal insulation, it is evident that as the simulation time increases, significant changes occur in the interface temperature, skin friction coefficient, heat flux distribution and separation bubble length, along the surface.
Future Work
Chantasiriwan S, (2002), Inverse determination of steady-state heat transfer coefficient, Journal of International Communications in Heat and Mass Transfer. Haji SA and Mashena M, (1987), Integral solution of the diffusion equation-part I-general solution, Transactions of ASME: Journal of Heat Transfer. Pagliarini G, (1991), Conjugate heat transfer for the simultaneous development of laminar flow in a circular pipe, Transactions of the ASME: Journal of Heat Transfer.
Taler J, (1996b), A semi-numerical method for solving the inverse heat conduction problem, International Journal of Heat and Mass Transfer. Woodbury KW, (1990), Effect of thermocouple sensor dynamics on surface heat flux predictions obtained via inverse heat transfer analysis, Journal of Heat and Mass Transfer.
