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1 
Orthogonal Decomposition Methods for Turbulent Heat Transfer Analysis with Application to Gas TurbinesSchwaenen, Markus 2011 May 1900 (has links)
Gas turbine engines are the main propulsion source for world wide aviation and are also used for power generation. Even though they rely mainly on fossil fuel and emit climate active gasses, their importance is not likely to decrease in the future. But more efficient ways of using finite resources and hence reducing emissions have to be found. Thus, the interest to improve engine efficiency is growing. Considering the efficiency of the underlying thermodynamic cycle, an increase can be achieved by raising the turbine inlet temperature or compression ratio. Due to the complex nature of the underlying flow physics, however, the aerothermal processes are still not fully understood. For this reason, one needs to perform research at high spatial and
temporal resolution, in turn creating the need for effective means of postprocessing the large amounts of data.
This dissertation addresses both sides of the problem  using highscale, high resolution simulations as well as effective post processing techniques. As an example for the latter, a temporal highly resolved data set from wall pressure measurements of a transonic compressor stage is analyzed using proper orthogonal decomposition. The underlying experiments were performed by collaborators at Technical University Darmstadt. To decompose signals into optimal orthogonal basis functions based on temporal correlations including temperature, a formal mathematical framework is developed. A method to rank the reduced order representations with respect to heat transfer effectiveness is presented. To test both methods, a Reynoldsaveraged NavierStokes (RANS) simulation and large eddy simulation (LES) are performed on turbulent heat transfer in a square duct with one single row of pin fins. While the LES results show closer agreement to experiments, both simulations unveil flow parts that do not contribute to heat transfer augmentation and can be considered wasteful. From the most effective mode, a wall contour for the same domain is derived and applied. In the wall contoured domain, energy in wasteful modes decreased, heat transfer increased and the temperature fluctuations at the wall decreased.
Another stagnating boundary layer flow is examined in a direct numerical simulation of a first stage stator vane. Elevated levels of free stream turbulence and integral length scale are generated to simulate the features of combustor exit flow. The horseshoe vortex dynamics cause an increase in endwall heat transfer upstream of the vane. The link between energy optimal orthogonal basis functions and flow structures is examined using this data and the reduced order heat transfer analysis shows high energy modes with comparatively low impact on turbulent heat transfer. The analysis further shows that there are multiple horseshoe vortices that oscillate upstream of the blade, vanish, regenerate and can also merge. There is a punctual correlation of intense vortex dynamics and peaks in the orthogonal temperature basis function.
For all data considered, the link between the energy optimal orthogonal basis functions and flow structures is neither guaranteed to exist nor straightforward to
establish. The orthogonal expansion locks onto flow parts with high fluctuating kinetic energy  which might or might not be the ones that are looked for. The heat
transfer ranking eliminates this problem and is valid independently of how certain basis functions are interpreted.

2 
Superstructures, heat and momentum transport in inclined turbulent thermal convection of lowPrandtlnumber fluidsZwirner, Lukas 03 June 2020 (has links)
No description available.

3 
Axially Homogeneous Turbulent Convection at High Rayleigh Numbers : Scaling Laws for Flux and SpectraPawar, Shashikant S January 2015 (has links) (PDF)
Natural turbulent convection studies encompass a wide range of flows occurring in nature, for example, atmospheric and oceanic flows, convection in the Earth’s mantle, convection in the stars and also in many engineering applications. RayleighBenard convection (RBC), i.e. convection in a horizontal fluid layer confined between two plates with a temperature diﬀerential maintained across them, has been a prototype problem in the studies of turbulent natural convection. Many small scale and global features of the flow in the turbulent regime of RBC are known, yet the flow dynamics is not fully understood, especially at high Rayleigh numbers (Ra). Present work comprises of experimental investigations of a diﬀerent type of flow, high Rayleigh number turbulent convection in a long vertical tube (abbreviated as tube convection or TC). The tube of aspect ratio (length to diameter) of about 10, open at both the ends interconnects two large tanks. The flow driven by an unstable density diﬀerence created between the two tanks, has some unique features, diﬀerent from RBC. The net flow at any tube crosssection is zero and the time averages of the velocities, the Reynolds shear stress and the mean shear are also zero. Turbulent energy production is therefore solely due to buoyancy. The flow is axially homogeneous and axisymmetric. In the homogeneous region, the mean density gradient is linear. Rayleigh number in TC is conveniently defined based on the mean (linear) density gradient (denoted by Rag).
Two sets of experiments are carried out. In one set of experiments, the density diﬀerence is created using brine and fresh water and in another set, it is created using heat. The ranges of Rag achieved are 3 × 108 < Rag < 8 × 109 in the experiments using salt (Schmidt
number, Sc ≈ 600) and 5 × 104 < Rag < 5 × 106 in the experiments using heat (Prandtl number, P r ≈ 6). From the measured salt and heat fluxes in both the sets of experiments, the non dimensional flux 1 1
scaling above a certain value of Rag is obtained as N ug ∼ Rag2 P r 2
and from the velocity measurements in the experiments using salt, the 1 Reynolds number scaling is obtained as Re ∼ Rag2 P r− 12 . Both these are as per the predicted scalings by the mixing length model proposed by Arakeri et al. (2000) for high Rag convection in the vertical tube.
The flux scaling N u ∼ (RaP r)2 , also known as the ‘ultimate regime’ of convection, expected at very high Ra but not yet observed in the experiments in classical RBC, is easily achieved in TC at relatively lower values of Ra. The fluxes and Reynolds numbers in TC are orders of magnitude higher as compared to those obtained in RBC for similar values of Ra and P r. In the lower range of Rag values for P r ≈ 6, a transition to a new flux scaling, N u ∼ (RaP r)0.29 is found. Similar transitions are also found to be present in the results of Tovar (2002) for
Sc ≈ 600 and in the DNS results of Schmidt et al. (2012) for P r = 1, at diﬀerent values of Rag. Collecting all these data, it is shown that the transition occurs at a fixed Grashof number of 1.6 × 105, independent of P r.
Velocity measurements are carried out using particle image velocimetry (PIV) in the salt experiments. Kinetic energy spectra computed from the velocity fields are presented for the locations from the tube axis to the wall, for the lowest and the highest values of Rag achieved in the experiments. The spatial energy spectrum of lateral velocity at the tube axis follows KolmogorovObukhov (KO) scaling (−5/3 scaling exponent) while the spatial spectrum of longitudinal velocity shows a scaling slightly higher than −5/3 but lower than −11/5 (the BolgianoObukhov (BO) scaling). The scalar spectra is computed from the concentration fields obtained from planar laser induced fluorescence (PLIF) in the experiments using salt, and also from the temperature measurements from the experiments using heat. Both the concentration and temperature fluctuations spectra show some evidence of dual scaling  BO scaling (−7/5 scaling exponent) in the inertial subrange
followed by ObukhovCorrsin (OC) scaling (−5/3 scaling exponent) over a narrow range of scales.
Light propagation through the buoyancy driven turbulent flow in TC has also been experimentally investigated. Light propagation through convective turbulence is encountered in many situations. In some cases e.g. in observational astronomy it is undesirable, while in some other cases it is useful, e.g. in remote sensing of meteorological parameters. In the present study, light intensity and angle of arrival fluctuations in a parallel beam of light are measured. Laser shadowgraphy is used in the intensity measurements while the angle of arrival is obtained by measuring deflections of narrow laser beams, created by passing collimated laser light through a mask having equispaced grid of holes. Background oriented schlieren (BOS) measurements have also been carried out to obtain the displacements, which are proportional to the angle of arrivals. The equations for frequency spectrum of intensity and angle of arrival from the literature, developed for isotropic, homogeneous turbulent media, are modified for the flow in the present case and the asymptotic scalings for high and low frequency ranges are obtained. The scalings in the frequency spectra computed from the measurements of intensity and angle of arrival fluctuations are compared with the obtained asymptotic scalings. The results from the present work are also compared with results from studies in the atmosphere and lab experiments.

4 
Investigations On High Rayleigh Number Turbulent Free ConvectionPuthenveettil, Baburaj A 06 1900 (has links)
High Rayleigh number(Ra) turbulent free convection has many unresolved
issues related to the phenomenology behind the flux scaling, the
presence of a mean wind and its effects, exponential probability
distribution functions, the Prandtl number dependence and the nature
of near wall structures. Few studies have been conducted in the high
Prandtl number regime and the understanding of near wall coherent
structures is inadequate for $Ra > 10^9$. The present thesis deals
with the results of investigations conducted on high Rayleigh
number turbulent free convection in the high Schmidt number(Sc)
regime, focusing on the role of near wall coherent structures.
We use a new method of driving the convection using concentration
difference of NaCl across a horizontal membrane between two tanks to
achieve high Ra utilising the low molecular diffusivity of NaCl. The
near wall structures are visualised by planar laser induced
fluorescence. Flux is estimated from transient measurement of
concentration in the top tank by a conductivity probe. Experiments
are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR =
0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of
0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine
membrane (and for the coarse membrane at low driving potentials), the
transport across the partition becomes diffusion dominated, while the
transport above and below the partition becomes similar to unsteady
non penetrative turbulent free convection above flat horizontal
surfaces (Figure~\ref{fig:schem}(A)). In this type of convection,
the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is
the near wall concentration difference, similar to that in Rayleigh 
B\'nard convection . Hence, we are able to study turbulent free
convection over horizontal surfaces in the Rayleigh Number range of
$\sim 10^ 10 ^$ at Schmidt number of 602, focusing on the
nature and role of near wall coherent structures. To our knowledge,
this is the first study showing clear images of near wall structures
in high Rayleigh Number  high Schmidt number turbulent free
convection.
We observe a weak flow across the membrane in the case of the coarser
membrane at higher driving potentials (Figure \ref(B)).
The effect of this through flow on the flux and the near wall
structures is also investigated. In both the types of convection the
near wall structure shows patterns formed by sheet plumes, the common
properties of these patterns are also investigated. The major
outcomes in the above three areas of the thesis can be summarised as
follows
\subsection*
\label
\subsubsection*
\label
The nondimensional flux was similar to that reported by
Goldstein\cite at Sc of 2750. Visualisations show that the near
wall coherent structures are line plumes. Depending on the Rayleigh
number and the Aspect ratio, different types of large scale flow cells
which are driven by plume columns are observed. Multiple large scale
flow cells are observed for AR = 0.65 and a single large scale flow
for AR= 0.435. The large scale flow create a near wall mean shear,
which is seen to vary across the cross section. The orientation of the
large scale flow is seen to change at a time scale much larger than
the time scale of one large scale circulation
The near wall structures show interaction of the large scale flow with
the line plumes. The plumes are initiated as points and then gets
elongated along the mean shear direction in areas of larger mean
shear. In areas of low mean shear, the plumes are initiated as points
but gets elongated in directions decided by the flow induced by the
adjacent plumes. The effect of near wall mean shear is to align the
plumes and reduce their lateral movement and merging. The time scale
for the merger of the near wall line plumes is an order smaller than
the time scale of the one large scale circulation. With increase in
Rayleigh number, plumes become more closely and regularly spaced.
We propose that the near wall boundary layers in high Rayleigh number
turbulent free convection are laminar natural convection boundary
layers. The above proposition is verified by a near wall model,
similar to the one proposed by \cite{tjfm}, based on the similarity
solutions of laminar natural convection boundary layer equations as
Pr$\rightarrow\infty$. The model prediction of the non dimensional
mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$  where
$Ra_\lambda$ is the Rayleigh number based on the plume spacing
$\lambda$, and $Z_w$ is a near wall length scale for turbulent free
convection  matches the experimental measurements. Therefore, higher
driving potentials, resulting in higher flux, give rise to lower mean
plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is
a constant for a given fluid.
We also show that the laminar boundary layer assumption is consistent
with the flux scaling obtained from integral relations. Integral
equations for the Nusselt number(Nu) from the scalar variance
equations for unsteady non penetrative convection are derived.
Estimating the boundary layer dissipation using laminar natural
convection boundary layers and using the mean plume spacing relation,
we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation
is only considered. The contribution of bulk dissipation is found to
be a small perturbation on the dominant 1/3 scaling, the effect of
which is to reduce the effective scaling exponent.
In the appendix to the thesis, continuing the above line of reasoning,
we conduct an exploratory reanalysis (for $Pr\sim 1$) of the Grossman
and Lohse's\cite scaling theory for turbulent Rayleigh  B\'enard
convection. We replace the Blasius boundary layer assumption of the
theory with a pair of externally forced laminar natural convection
boundary layers per plume. Integral equations of the externally forced
laminar natural convection boundary layer show that the mixed
convection boundary layer thickness is decided by a $5^{th}$ order
algebraic equation, which asymptotes to the laminar natural convection
boundary layer for zero mean wind and to Blasius boundary layer at
large mean winds.
\subsubsection*{Effect of wall normal flow on flux and near wall structures}
\label{sec:effectwallnormal}
For experiments with the coarser($35\mu$) membrane, we observe three
regimes viz. the strong through flow regime
(Figure~\ref{fig:schem}(b)), the diffusion regime (Figure
\ref{fig:schem}(a)), and a transition regime between the above two
regimes that we term as the weak through flow regime.
At higher driving potentials, only half the area above the coarser
membrane is covered by plumes, with the other half having plumes below
the membrane. A wall normal through flow driven by impingement of the
large scale flow is inferred to be the cause of this (Figure
\ref{fig:schem}(b)). In this strong through flow regime, only a single
large scale flow circulation cell oriented along the diagonal or
parallel to the walls is detected. The plume structure is more
dendritic than the no through flow case. The flux scales as $\Delta
C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed
with the fine membrane. The phenomenology of a flow across the
membrane driven by the impingement of the large scale flow of strength
$W_*$, the Deardorff velocity scale, explains the cubic scaling. We
find the surprising result that the nondimensional flux is smaller
than that in the no through flow case for similar parameters.
The mean plume spacings in the strong through flow regime are larger
and show a different Rayleigh number dependence visavis the no
through flow case. Using integral analysis, an expression for the
boundary layer thickness is derived for high Schmidt number laminar
natural convection boundary layer with a normal velocity at the wall.
(Also, solutions to the integral equations are obtained for the
$Sc\sim 1$ case, which are given as an Appendix.) Assuming the
gravitational stability condition to hold true, we show that the plume
spacing in the high Schmidt number strong through flow regime is
proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length
scale from the through flow velocity. This inference is fairly
supported by the plume spacing measurements
At lower driving potentials corresponding to the transition regime,
the whole membrane surface is seen to be covered by plumes and the
flux scaled as $\Delta C_w^{4/3}$.
The nondimensional flux is about the same as in turbulent free
convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to
occur on one side of the membrane. This is expected to occur in the
area averaged sense with different parts of the membrane having
predominance of diffusion or through flow dominant transport. At very
low driving potentials corresponding to the diffusion regime, the
diffusion corrected non dimensional flux match the turbulent free
convection values, implying a similar phenomena as in the fine
membrane.
\subsubsection*{Universal probability distribution of near wall structures}
\label{sec:univprobdistr}
We discover that the probability distribution function of the plume
spacings show a standard log normal distribution, invariant of the
presence or the absence of wall normal through flow and at all the
Rayleigh numbers and aspect ratios investigated. These plume
structures showed the same underlying multifractal spectrum of
singularities in all these cases. As the multifractal curve indirectly represents the processes by which
these structures are formed, we conclude that the plume structures are created by a common
generating mechanism involving nucleation at points, growth along
lines and then merging, influenced by the external mean shear.
Inferring from the thermodynamic analogy of multifractal analysis, we
hypothesise that the near wall plume structure in turbulent free
convection might be formed so that the entropy of the structure is
maximised within the given constraints.

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