rexresearch.com
ClearSign : Electrodynamic
Combustion Control
US2011203771
METHOD AND APPARATUS FOR ELECTRICAL CONTROL OF HEAT
TRANSFER
A heat exchange system includes an electrode configured to
electrostatically control a flow of a heated gas stream in the
vicinity of a heat transfer surface and/or a heat-sensitive
surface.
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims priority benefit under 35
USC §119(e) to U.S. Provisional Application Ser. No. 61/294,761;
entitled “METHOD AND APPARATUS FOR ELECTRICALLY ACTIVATED HEAT
TRANSFER”, invented by David Goodson, Thomas S. Hartwick, and
Christopher A. Wiklof, filed on Jan. 13, 2010, which is currently
co-pending herewith, and which, to the extent not inconsistent
with the disclosure herein, incorporated by reference.
BACKGROUND
[0002] Typical external combustion systems such as combustors and
boilers may include relatively complicated systems to maximize the
extraction of heat from a heated gas stream. Generally, such
systems may rely on forced or natural convection to transfer heat
from the heated gas stream through heat transfer surfaces to heat
sinks.
[0003] Other systems, which may include the combustion systems
indicated above, or may include other systems such as turbo-jet
engines, ram- or scram-jet engines, and rocket engines, for
example, are limited with respect to combustion temperature or
reliability due to erosion of critical parts by hot gases. It
would be desirable to reduce heat transfer to
temperature-sensitive surfaces of such systems.
SUMMARY
[0004] According to an embodiment, a system for electrically
stimulated heat transfer may include at least one first electrode
positioned adjacent to a heated gas stream, and at least one heat
transfer surface positioned near the at least one electrode. The
heated gas stream may include positively and/or negatively charged
species evolved from a combustion reaction. At least one first
electrode may be electrically modulated to attract the positively
and/or negatively charged species toward the at least one heat
transfer surface. The attracted charged species may entrain
heat-bearing non-charged species. The flow of heat-bearing charged
and non-charged species may responsively flow near the at least
one heat transfer surface and transfer heat energy from the heated
gas stream to a heat sink corresponding to the at least one heat
transfer surface.
[0005] According to another embodiment, at least one second
electrode may selectively remove one or more charged species from
the heated gas stream. The heated gas stream may thus exhibit a
charge imbalance that may be maintained as the heated gas stream
flows in the vicinity of the at least one first electrode.
[0006] According to another embodiment a heat transfer surface may
include an integrated electrode configured for electrostatic
attraction of charged species in a heated gas stream. The
attracted charged species may entrain heated non-charged species.
The integrated electrode may be electrically isolated from the
heat transfer surface.
[0007] According to another embodiment, a method for stimulating
heat transfer may include providing a heated gas carrying
electrically charged species, modulating a first electrode to
drive the heated gas to flow adjacent to a heat transfer surface,
and transferring heat from the gas to the heat transfer surface.
[0008] According to another embodiment, a method for protecting a
temperature-sensitive surface may include providing a heated gas
carrying electrically charged species and modulating a first
electrode to drive the heated gas to flow distal from a
temperature-sensitive surface to reduce the transfer of heat from
the gas to the temperature-sensitive surface.
[0009] According to another embodiment, an apparatus for reducing
heat transfer from a combustion reaction may include a
temperature-sensitive surface positioned in a hot gas stream
including electrically charged species from a combustion reaction
and a first electrode configured to be modulated to drive the
electrically charged species from the combustion reaction to a
location away from the temperature-sensitive surface.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a diagram of a system configured to
stimulate heat transfer to a heat transfer surface using an
electric field, according to an embodiment.
[0011] FIG. 2 is a diagram of a system having alternative
electrode arrangement compared to the system of FIG. 1,
according to an embodiment.
[0012] FIG. 3 is a partial cross section of an integrated
electrode and heat transfer surface corresponding to FIG. 2,
according to an embodiment.
[0013] FIG. 4 is a waveform diagram showing illustrative
waveforms for driving electrodes of FIGS. 1-3, according to an
embodiment.
[0014] FIG. 5 is a diagram of a system configured with a
plurality of electrodes and heat transfer surfaces, according to
an embodiment.
[0015] FIG. 6 is a close-up sectional view of a heat
transfer surface illustrating an effect of impinging charged
species on a boundary layer, according to an embodiment.
[0016] FIG. 7 is a diagram of a system configured to
protect a heat-sensitive surface from heat transfer using an
electric field, according to an embodiment.
[0017] FIG. 8 is a diagram of a system configured to
protect a heat-sensitive surface from heat transfer using an
electric field, according to another embodiment.
DETAILED DESCRIPTION
[0018] In the following detailed description, reference is
made to the accompanying drawings, which form a part hereof. In
the drawings, similar symbols typically identify similar
components, unless context dictates otherwise. The illustrative
embodiments described in the detailed description, drawings, and
claims are not meant to be limiting. Other embodiments may be
utilized, and other changes may be made, without departing from
the spirit or scope of the subject matter presented here.
[0019] FIG. 1 is a diagram of a system 101 configured to stimulate
heat transfer to a heat transfer surface 114 using an electric
field, according to an embodiment. The system 101 may typically
include a flame 102 supported by a burner assembly 103. A
combustion reaction in the flame 102 generates a heated gas 104
(having a flow illustrated by the arrow 105) carrying electrically
charged species 106, 108. Typically, the electrically charged
species include positively charged species 106 and negatively
charged species 108.
[0020] Providing a heated gas carrying charged species 106, 108
may include burning at least one fuel from a fuel source 118, the
combustion reaction providing at least a portion of the charged
species and combustion gasses. According to some embodiments, the
combustion reaction may provide substantially all the charged
species 106, 108.
[0021] The charged species 106, 108 may include unburned fuel;
intermediate radicals such as hydride, hydroperoxide, and hydroxyl
radicals; particulates and other ash; pyrolysis products; charged
gas molecules; and free electrons, for example. At various stages
of combustion, the mix of charged species 106, 108 may vary. As
will be discussed below, some embodiments may remove a portion of
the charged species 106 or 108 in a first portion of the heated
gas 104, leaving a charge imbalance in another portion of the
heated gas 104.
[0022] For example, one embodiment may remove a portion of
negative species 108 including substantially only electrons,
leaving a positive charge imbalance in the gas stream 104.
Positive species 106 and remaining negative species 108 may then
be electrostatically attracted to the vicinity of a heat sink 116,
resulting in a stimulation of heat transfer. Alternatively, a
portion of positive species 106 may be removed from the heated gas
stream 104, leaving a negative charge imbalance in the gas stream.
[0023] A first electrode 110 may be voltage modulated by a voltage
source 112. The voltage modulation may be configured to attract a
portion of the charged species 106, here illustrated as positive.
Modulating the first electrode may include driving the first
electrode to one or more voltages selected to attract oppositely
charged species, and the attracted oppositely charged species
imparting momentum transfer to the heated gas.
[0024] The momentum transfer from the electrically driven charged
species 106 may be regarded as entraining non-charged particles,
unburned fuel, ash, etc. carrying heat. The modulated first
electrode 110 may be configured to attract the charged species and
other entrained species carrying heat to preferentially flow
adjacent to a heat transfer surface 114. As the heat-carrying
species flow adjacent to the heat transfer surface 114, a portion
of the heat carried by the species is transferred through the heat
transfer surface 114 to a heat sink 116.
[0025] According to an embodiment, the first electrode 110 may be
arranged near the heat transfer surface 114. A nominal mass flow
105 may be characterized by a velocity (including speed and
direction). The first electrode 110 may be configured to impart a
drift velocity to the charged species 106 at an angle to the
nominal mass flow velocity 105 and toward the heat transfer
surface 114.
[0026] As mentioned above, the system 101 may further modulate at
least one second electrode 120 to remove a portion of the charged
species 106, 108. According to an embodiment, the second electrode
120 may preferentially purge negatively-charged species 108 from
the heated gas 104. According to an embodiment, the second
electrode may preferentially purge a portion of electrons 108 from
the heated gas 104.
[0027] According to an embodiment, the at least one second
electrode 120 includes a burner assembly 103 that supports a flame
102, the flame 102 providing a locus for the combustion reaction.
The second electrode 120 may be driven with a waveform from the
voltage source 112. Alternatively, the second electrode may be
driven from another voltage source.
[0028] While the flame 102 is illustrated in a shape typical of a
diffusion flame, other combustion reaction distributions may be
provided, depending upon a given embodiment.
[0029] FIG. 2 is a diagram of a system 201 having alternative
electrode arrangement compared to the system 101 of FIG. 1,
according to an embodiment. The system 201 may include a first
electrode 110 that is integrated with the heat transfer surface
114. The system 201 may additionally or alternatively include an
optional second electrode 120 that is separate from the burner
assembly 103. As with the system 101 of FIG. 1, the burner
assembly 103 is configured to support a flame 102 that provides a
locus for combustion and generation of at least a portion of the
charged particles 106, 108 carried in the heated gas 104.
[0030] A heat sink 116 may be positioned in the heated gas stream
104 as illustrated. As the heated gas stream flows past the heat
sink 116, the flow may split, as illustrated by the arrows 105.
According to an embodiment, at least one electrode 110, here
illustrated as being integrated with the heat transfer surface 114
adjoining the heat sink 116, may be modulated to electrostatically
attract charged species 106 and/or 108. As may be appreciated,
such attraction may tend to move the charged species 106, 108
along paths at angles to the mean gas flow velocity 105.
[0031] One possible outcome of carrying positive 106 and negative
108 species through the entirety of the heated gas stream 104 is
recombination, whereby a positive charge 106 combines with a
negative charge 108 to produce one or more neutral species (not
shown). Such recombination may reduce the coupling efficiency
between the first electrode 110 and the heated gas 104 by reducing
the concentration of charged species 106 responsive to a voltage
on the first electrode 110.
[0032] As with the description corresponding to FIG. 1, the
placement of a positive species attractive electrode (e.g. the
first electrode 110) and negative species attractive electrode
(e.g. the second electrode 120) represents an embodiment. Other
embodiments may reverse the relationship and/or otherwise modify
the embodiment of FIG. 2 without departing from the spirit or
scope of this description.
[0033] According to the embodiment 201, the at least one second
electrode 120 includes an electrode positioned at a location
nearer the burner assembly 103 than the distance between the
burner assembly 103 and the heat transfer surface 114. For
example, the at least one second electrode 120 may be positioned
and driven to sweep electrons 108 out of the flow of the heated
gas 104. The modulation of the at least one second electrode 120
may include providing an alternating voltage. The voltage to which
the voltage driver 112 drives the second electrode 120 may attract
the electrons 108 to the surface of the second electrode 120. The
electrons 108 may combine with a positively charged conductor
including the at least one second electrode 120 and thus be
removed from the heated gas stream 104.
[0034] While the open cylindrical or toric shape of the second
electrode 120 represents one embodiment, alternative shapes may be
appropriate for alternative embodiments.
[0035] In the embodiment 201, the heat transfer surface 114
includes the first electrode 110. FIG. 3 is a partial cross
section of an apparatus 301 including an integrated electrode 110
and heat transfer surface 114 corresponding to FIG. 2, according
to an embodiment.
[0036] According to an embodiment, the integrated apparatus 301
may form at least a portion of a wall of a fire tube or water tube
boiler, for example. For example, the heat transfer surface 114
may include a tube or pipe wall that includes an opposing surface
302 abutting a heat sink 116. The heat sink 116 may include a
flowing liquid, vapor, and/or steam. Alternatively, the heat
transfer surface may separate a heated gas stream 104 from a
convective or forced air heat sink 116, such as in an air-to-air
heat exchanger. According to another embodiment, the heat sink 116
may represent a solid heat conductor, a heat pipe, or other
apparatus that is configured to be heated by the heated gas 104.
According to some embodiments, the heat transfer surface may
include the surface of a heat sink 116 that is substantially solid
of a heat conductor, and there may be substantially no opposite
wall 302. In some embodiments, such as in the case of a fire tube
boiler embodiment for example, the radius depicted in FIG. 3 may
be flattened or reversed.
[0037] According to some embodiments, it may be desirable to
provide an apparatus 301 including an integrated electrode 110 and
heat transfer surface 114 wherein the electrode 110 is
electrically isolated from the heat transfer surface 114. The
embodiment 301 may include a thermally conductive wall extending
from the heat transfer surface 114. The thermally conductive wall
may extend to an opposite surface 302 or may extend to an
extension of the heat transfer surface 114 (such as in a
cylindrical heat sink 116) or may extend to an opposite surface
that is discontinuous from the heat transfer surface 114, but
which is adiabatic.
[0038] An electrical insulator 304 may be disposed over at least a
portion of the thermally conductive wall extending from the heat
transfer surface 114. The first electrode 110 may include an
electrically conductive layer disposed over at least a portion of
the electrical insulator 304.
[0039] Various electrical insulators 302 may be used. According to
embodiments, the electrical insulator 302 may be selected for a
relatively high dielectric constant (at least at a modulation
frequency of the first electrode 110), a melting point or glass
transition temperature high enough to avoid degradation, a
relatively high thermal conductivity, a relatively low coefficient
of thermal expansion, and/or a coefficient of thermal expansion
that is relatively well-matched to that of the material in the
wall extending from the heat transfer surface 114 and/or the
electrode layer 110. For example, the electrical insulator 304 may
include one or more of polyether-ether-ketone, polyimide, silicon
dioxide, silica glass, alumina, silicon, titanium dioxide,
strontium titanate, barium strontium titanate, or barium titanate.
Lower dielectric materials such as polyimide,
polyether-ether-ketone, silicon dioxide, silica glass, or silicon
may be most appropriate for the insulation layer for embodiments
using lower voltages and/or greater insulator thicknesses.
[0040] According to embodiments, the conductive layer of the
electrode 110 may be selected to have relatively high conductivity
and relatively high melting point. For example, the first
electrode 110 may include one or more of graphite, chromium, an
alloy including chromium, an alloy including molybdenum, tungsten,
an alloy including tungsten, tantalum, an alloy including
tantalum, or niobium-doped strontium titanate.
[0041] According to some embodiments, the at least one electrode
110 may include a portion that is deposited prior to operation,
e.g. a metal, crystal, or graphite, and a portion that is
deposited during operation, for example carbon particles such as
conductive soot or conductive ash. A useful dynamic may occur when
a portion of the conductivity of the at least one electrode 110
accrues from a deposit formed during operation. Electrodes or
electrode regions that exhibit increased coupling efficiency, for
example owing to system geometry, power output, stoichiometry,
and/or fuel flow/heated air flow rate, may tend to attract a
relatively greater particle impingement. The relatively greater
particle impingement may tend to erode or displace the deposited
matter. The removal of the deposited matter that forms a portion
of the electrode may result in a decrease in coupling efficiency
to the heated gas 104. The resultant decrease in coupling
efficiency may reduce the amount of particle impingement, and
hence erosion. According to an embodiment, these effects may help
to provide a pseudo-equilibrium that may equalize “pull” on
charged particles across the extent of an electrode or across an
array of electrodes.
[0042] Referring back to FIGS. 1 and 2, the voltage source 112 may
be configured to drive the at least one first electrode 110, and
optionally at least one second electrode 120 with electrical
waveforms. As indicated above, modulating the at least one first
electrode 110 may include driving the first electrode 110 to one
or more voltages selected to attract oppositely charged species
106, 108, and the attracted oppositely charged species may then
impart momentum transfer to the heated gas. An optional at least
one second electrode 120 may be driven with a waveform selected to
at least partially sweep some of the charged species 106, 108,
such as electrons 108, out of the flow of the heated gas 104. The
electrical waveforms that drive the at least one first electrode
110 and the optional at least one second electrode 120 may include
a dc voltage waveform, an ac voltage waveform, an ac voltage with
dc bias, non-periodic fluctuating waveforms, and/or combinations
thereof.
[0043] FIG. 4 is a waveform diagram 401 showing illustrative
waveforms for driving electrodes 110, 120 of FIGS. 1-3, according
to an embodiment. The waveform 402 depicts an illustrative
approach to driving the at least one first electrode 110. For
multiple electrode 110 systems, a common waveform 402 may drive
all the electrodes 110. Alternatively, one or more of the multiple
electrodes 110 may be driven by a waveform 402 different from
other waveforms 402 used to drive the other multiple electrodes
110.
[0044] According to an embodiment, the waveform 402 may modulate
between a high voltage VH and a low voltage VL in a pattern
characterized by a period P1. The high voltage VH and low voltage
VL may be selected as equal magnitude variations above and below a
mean voltage V01. The mean voltage V01 may be a ground voltage or
may be a constant or variable voltage V01 representing a dc bias
from ground. The absolute value |VH-V01|=|VL-V01| may be greater
than, less than, or about equal to the absolute value |V01|. In
other words, the high voltage VH may be above, about equal to, or
below ground, depending on the embodiment. Similarly, the low
voltage VL may be above, about equal to, or below ground,
depending on the embodiment.
[0045] The period P1 includes a duration tL corresponding to the
low voltage VL and another duration tH corresponding to the high
voltage VH. According to some embodiments tL+tH=P1. According to
other embodiments (not shown), the period may include a portion of
time during which the voltage may be held at the mean voltage V01,
to yield tL+tH<P1. For embodiments where VL is below ground, a
positive species duty cycle D+ may be defined as D+=tL/(tL+tH).
Similarly, for embodiments where VH is above ground, a negative
species duty cycle D- may be defined as D-=tH/(tL+tH). For a
single electrode 110, the positive species duty cycle D+ and the
negative species duty cycle D- are not linearly independent.
However, linearly independent positive species and negative
species duty cycles, D+, D- may be provided by spatially separated
electrodes 110.
[0046] For the embodiments 110, 210 illustrated in FIGS. 1 and 2,
and assuming constant VL<0 and constant VH>0, effects of a
waveform 402 will be described. During period P1 portions tL, the
electrode 110 provides an electrostatic attraction to positive
species 106 in the heated gas stream 104 and imparts a drift
velocity on the positive species 106 toward the electrode 110. The
drift velocity may be at an angle to the mass flow velocity 105
when the electrode 110 is positioned lateral to the mass flow
velocity 105. During portions tL, the electrode 110 may tend to
repel negative species 108 entrained within the heated gas stream
104.
[0047] During period P1 portions tH, the electrode 110 provides an
electrostatic attraction to negative species 108 in the heated gas
stream 104 and imparts a drift velocity on the negative species
108 toward the electrode 110. The drift velocity may be at an
angle to the mass flow velocity 105 when the electrode 110 is
positioned lateral to the mass flow velocity 105. During portions
tH, the electrode 110 may tend to repel positive species 106
entrained within the heated gas stream 104.
[0048] For a substantially constant VL, a larger positive species
duty cycle D+ provides a greater amount of positive species 106
attraction and a lower positive species duty cycle D+ provides a
lesser amount of positive species 106 attraction. The positive
species duty cycle D+provided by the voltage source 112 may be
varied according to the amount of drift momentum desired to be
impressed upon the heated gas stream 104. For example, at a higher
flow rate 105, a higher positive species duty cycle D+ may be
useful for maximizing positive species 106 flux, and hence
maximizing heat extraction from the heated gas 104.
[0049] Similarly, for a substantially constant VH, a larger
negative species duty cycle D- provides a greater amount of
negative species 108 attraction, and a lower negative species duty
cycle D- provides a lesser amount of negative species 108
attraction. The negative species duty cycle D- provided by the
voltage source 112 may be varied according to the amount of drift
momentum desired to be impressed upon the heated gas stream 104.
For example, at a higher flow rate 105, a higher negative species
duty cycle D- may be useful for maximizing negative species 108
flux, hence maximizing heat extraction from the heated gas 104.
[0050] The period P1 may be selected according to a range of
considerations. For example, the concentration of positive and/or
negative species 106, 108 in the heated gas stream may at least
partly determine an effective impedance and/or conductivity
related to an effective relative dielectric constant, which may,
in turn, affect a frequency-dependence of the electrostatic
coupling efficiency to the heated gas 104. According to another
example, the mass/charge ratio of the positive and/or negative
species may affect their frequency dependent momentum response to
the waveform 402. Other things being equal, larger period P1 may
provide higher electrostatic coupling efficiency to more massive
species 106, 108. A shorter period P1, on the other hand, may be
advantageous for avoiding arcing, especially when voltages VH
and/or VL have large absolute magnitudes relative to grounded
surfaces abutting the heated gas 104.
[0051] Depending on the mix of positive species 106 and negative
species 108 in the vicinity of the at least one electrode 110 and
the heat transfer surface 114, one or the other of the positive
species duty cycle D+ or the negative species duty cycle D- may be
of greater importance for increasing the heat flux to the heat
transfer surface 114. As described above, at least one second
electrode 120, which may be positioned nearer the burner assembly
103 and combustion locus 102 than the at least one first electrode
110, may be used to purge a portion of charged species 106 or 108
from the heated gas 104. Purging a portion of the charged species
106 or 108 from the heated gas 104 may tend to reduce charge
recombination and corresponding reduction in charged species 106
or 108 present while the heated gas traverses a region in the
vicinity of the at least one first electrode 110 and heat transfer
surface 114. Additionally, purging a portion of charged species
106 or 108 may result in a charge imbalance in the vicinity of the
at least one electrode 110 and the heat transfer surface 114. The
charge imbalance may be used to advantage by preferentially
attracting the higher concentration species.
[0052] For example, electrons 108 may be swept out of the heated
gas 104 by at least one second electrode 120. Returning again to
FIG. 4, waveform 404 illustrates a waveform that may be provided
by the voltage source 112 to the at least one second electrode 120
to sweep one or more charged species out of the heated air column
104. For example, the at least one second electrode may sweep
electrons out of the gas stream 104, resulting in a positive
charge imbalance in the vicinity of the at least one first
electrode 110 and the heat transfer surface 114. The electrons may
combine with a positively charged conductor including the at least
one second electrode 120 and thereafter be conducted away to the
voltage source 112.
[0053] According to an embodiment, the waveform 404 may modulate
between a high voltage VH2 and a low voltage VL2 in a pattern
characterized by a period P2. The high voltage VH2 and low voltage
VL2 may be selected as equal magnitude variations above and below
a mean voltage V02. The mean voltage V02 may be a ground voltage
or may be a constant or variable voltage V02 representing a dc
bias from ground. The absolute value |VH2-V02|=|VL2-V02| may be
greater than, less than, or about equal to the absolute value
|V02|. In other words, the high voltage VH2 may be above, about
equal to, or below ground, depending on the embodiment. Similarly,
the low voltage VL2 may be above, about equal to, or below ground,
depending on the embodiment.
[0054] The period P2 includes a duration tL2 corresponding to the
low voltage VL2 and another duration tH2 corresponding to the high
voltage VH2. According to some embodiments tL2+tH2=P2. According
to other embodiments (not shown), the period may include a portion
of time during which the voltage may be held at the mean voltage
V02, to yield tL2+tH2<P2. For embodiments where VL2 is below
ground, a positive species duty cycle D+2 may be defined as
D+2=tL2/(tL2+tH2). Similarly, for embodiments where VH2 is above
ground, a negative species duty cycle D-2 may be defined as
D-2=tH2/(tL2+tH2). For a single electrode 120, the positive
species duty cycle D+2 and the negative species duty cycle D-2 are
not linearly independent. However, linearly independent positive
species and negative species duty cycles, D+2, D-2 may be provided
by spatially separated electrodes 120.
[0055] For the embodiments 110, 210 illustrated in FIGS. 1 and 2,
and assuming constant VL2<0 and constant VH2>0, effects of a
waveform 404 will be described. During period P2 portions tL2, the
electrode 120 provides an electrostatic attraction to positive
species 106 in the heated gas stream 104 and imparts a drift
velocity on the positive species 106 toward the electrode 120. The
drift velocity may be at an angle to the mass flow velocity 105
when the electrode 120 is positioned lateral to the mass flow
velocity 105. During portions tL2, the electrode 120 may tend to
repel negative species 108 entrained within the heated gas stream
104.
[0056] During period P2 portions tH2, the electrode 120 provides
an electrostatic attraction to negative species 108 in the heated
gas stream 104 and imparts a drift velocity on the negative
species 108 toward the electrode 120. The drift velocity may be at
an angle to the mass flow velocity 105 when the electrode 120 is
positioned lateral to the mass flow velocity 105. During portions
tH2, the electrode 120 may tend to repel positive species 106
entrained within the heated gas stream 104.
[0057] For a substantially constant VL2, a larger positive species
duty cycle D+2 provides a greater amount of positive species 106
attraction and a lower positive species duty cycle D+2 provides a
lesser amount of positive species 106 attraction. The positive
species duty cycle D+2 provided by the voltage source 112 may be
varied according to the amount of positive species 106 desired to
be removed from the heated gas stream 104. For example, at a
higher flow rate 105, a higher positive species duty cycle D+2 may
be useful for maximizing positive species 106 flux, and hence
maximizing the withdrawal of positive species from the heated gas
104.
[0058] Similarly, for a substantially constant VH2, a larger
negative species duty cycle D-2 provides a greater amount of
negative species 108 attraction, and a lower negative species duty
cycle D-2 provides a lesser amount of negative species 108
attraction. The negative species duty cycle D-2 provided by the
voltage source 112 may be varied according to the amount of
negative species to be removed from the heated gas stream 104. For
example, at a higher flow rate 105, a higher negative species duty
cycle D-2 may be useful for maximizing negative species 108 flux,
hence maximizing negative species extraction from the heated gas
104.
[0059] The period P2 may be selected according to a range of
considerations. For example, the concentration of positive and/or
negative species 106, 108 in the heated gas stream may at least
partly determine an effective impedance and/or conductivity
related to an effective relative dielectric constant, which may,
in turn, affect a frequency-dependence of the electrostatic
coupling efficiency to the heated gas 104. According to another
example, the mass/charge ratio of the positive and/or negative
species may affect their frequency dependent momentum response to
the waveform 404. Other things being equal, larger period P2 may
provide higher electrostatic coupling efficiency to more massive
species 106, 108. A shorter period P2, on the other hand, may be
advantageous for avoiding arcing or avoiding the undesirable
removal of move massive charged species 106, 108, especially when
voltages VH2 and/or VL2 have large absolute magnitudes relative to
grounded surfaces abutting the heated gas 104.
[0060] According to an illustrative embodiment, at least one
second electrode 120 may be configured to sweep a portion of
electrons from the heated gas 104, but avoid sweeping other
negative species from the heated gas 104. For example, the period
P2 of the second electrode modulation may be selected to impart
sufficient momentum on electrons to withdraw a portion of the free
electrons. More massive negative particles respond (accelerate)
more slowly to the force imparted by the electrical field because
of the inverse mass relationship between force and acceleration.
Hence, a relatively short period P2 may result in an acceleration
of electrons to the surface of the second electrode, but leave
more massive negative species in the heated gas 104.
[0061] At least one first electrode 110 may be configured to
primarily drive remaining and relatively massive positive species
including unburned fuel and ash toward a heat transfer surface
114. For example, for a system including a 7.6 cm diameter tube
enclosing the heated volume and a heated gas 104 velocity of about
90 cm/second, the at least one first electrode 110 may be
modulated between about 0 volts and -10,000 volts at a frequency
of about 300 Hz at a 97% duty cycle. This results in the at least
one first electrode 110 being periodically modulated to -10 kV for
3.22 milliseconds and then to 0V for 0.1 milliseconds, for a total
period of 3.32 milliseconds (301.2 Hz).
[0062] According to an embodiment, the at least one first
electrode 110 may produce an electric field strength of about 1
kV/cm. Because of the large number of collisions between species
in the heated gas 104, acceleration may be ignored and moderate
mass positively charged species 106 (e.g. CO<+>,
C3H8<+>, etc.) in the stream (along with entrained gas and
particles) may be approximated to be imparted with a nominal drift
velocity toward the first electrode 110 (and hence the heat
transfer surface 114) of about 1000 cm/second. In comparison to an
embodiment having a typical gas flow rate of about 100 cm/second,
one may appreciate that driving the at least one first electrode
110 may significantly affect the transfer of heat through the heat
transfer surface 114.
[0063] At least one second electrode 120 may be configured to
primarily drive electrons out of the heated gas 104. For example
for a system using a burner nozzle as the second electrode 120
centered in a 7.6 cm diameter tube and a heated gas velocity of
about 90 cm/second, the second electrode 120 may be modulated
between about 0 volts and +10,000 volts at a frequency of about
300 Hz at a 97% duty cycle. This results in the at least one
second electrode 120 being periodically modulated to +10 kV for
3.22 milliseconds and then to 0V for 0.1 milliseconds, for a total
period of 3.32 milliseconds (301.2 Hz). Another second electrode
120 modulation schema may provide 50% duty cycle modulation
between 0V and +10,300V at a frequency of 694.4 kHz.
[0064] According to an embodiment, the at least one second
electrode 120 may produce an electric field strength of about 1
kV/cm. Because of the large number of collisions between species
in the heated gas 104, acceleration may be ignored and low mass
negatively charged species 106 (e.g. e<->) in the stream may
be approximated to be imparted with a nominal drift velocity
toward the second electrode 120 of about 10<5 >cm/second,
which is more than sufficient to overcome an illustrative gas flow
rate of 100 cm/sec. However, because of the low mass of electrons,
relatively little momentum is transferred to other species in the
heated gas 104, thus avoiding entrainment, and significant flow of
heat to the second electrode 120 may be avoided.
[0065] FIG. 5 is a diagram of a system 501 configured with a
plurality of first electrodes 110a, 110b and heat transfer
surfaces 114a, 114b, 114c, according to an embodiment. The
plurality of first electrodes 110a-b and heat transfer surfaces
114a-c may be arranged to respectively drive and receive heat
transfer from a heated gas stream 104 generated by at least one
combustion locus or flame 102 supported by at least one burner
assembly 103. The at least one combustion reaction supported by
the at least one burner assembly 103 may evolve positively charged
species 106 and negatively charged species 108 into the heated gas
stream 104.
[0066] The plurality of first electrodes may be driven with a
common waveform from a voltage source 112 or with separate
waveforms. The plurality of first electrodes 110a, 110b may be
configured to impart drift velocities to the positively charged
species 106 and/or the negatively charged species 108 at a
plurality of angles to a nominal mass flow velocity 105. A heat
transfer surface may include a plurality of heat transfer surfaces
114a-c. The plurality of heat transfer surfaces 114a-c may
correspond to a common heat sink or to a corresponding plurality
of heat sinks 116a-c.
[0067] For example, a common heat sink 116a may correspond to a
water tube in a boiler. The water tube may, for example, include
an electrically insulating layer (not shown) formed over
substantially the entirety of the water tube. A plurality of
electrodes 110a-b may be formed as patterned conductors over the
insulating layer (not shown) on the water tube 116a. The plurality
of heat transfer surfaces 114a-c may correspond to regions between
the patterned electrodes 110a-b.
[0068] According to an alternative embodiment, the plurality of
heat transfer surfaces 114a-c may correspond to a plurality of
heat sinks 116a-c. For example, at least a portion of the
plurality of first electrodes 110a, 110b may be interdigitated
with at least a portion of the plurality of heat transfer surfaces
114a-c. The heat sinks 116a-c and heat transfer surfaces 114a-c
may optionally be electrically conductive. The plurality of first
electrodes 110a-b may be separated from the heat transfer surfaces
114a-c by air gaps. The air gaps may insulate the plurality of
first electrodes 110a-b from the plurality of heat transfer
surfaces 114a-c and/or the plurality of heat sinks 116a-c.
[0069] A plurality of heat transfer surfaces 114a-c and
corresponding plurality of heat sinks 116a-c may form a heat sink
array 502. A system 501 may include a plurality of heat sink
arrays 502, 502b, 502c. The heat sink arrays 502, 502b, 502c may
include electrodes driven by a common voltage source 112, or by a
corresponding plurality of voltage sources (not shown).
[0070] FIG. 6 is a close-up sectional view 601 of heat transfer
surfaces 114a, 114b illustrating an effect of impinging charged
species 106, 108 (and any entrained non-charged species) on
boundary layers 602a, 602b, according to an embodiment. A heated
gas stream 104 includes a bulk flow velocity 105. Heat transfer
surfaces 114a, 114b may be disposed adjacent to the heated gas
stream 104.
[0071] A first heat transfer surface 114a, may not include a
corresponding electrode, or may represent a moment during which a
corresponding electrode is not modulated to attract a charged
species. A boundary layer 602a lies over the heat transfer surface
114a. The boundary layer 602a may represent a thickness of
relatively quiescent air across which thermal diffusion and/or
radiation may dominate as heat transfer mechanisms over convective
heat transfer. Even in cases where the heated air stream 104 as a
whole is moving with sufficient velocity 105 to provide convective
heat transfer, for example as turbulent flow, the boundary layer
602a may be present. In cases where the heated air average
velocity 105 is high enough to reach a Reynolds number
characteristic of turbulent flow, the boundary layer 602a may be
characterized as a turbulent boundary layer.
[0072] Convective heat transfer and/or heat transfer between
regions outside the boundary layer 602a is characterized by a
higher heat transfer coefficient than heat transfer across the
boundary layer 602a. The thickness of the boundary layer 602a may
be proportional to its resistance to heat transfer from the heated
air stream 104 to the heat transfer surface 114a.
[0073] A second heat transfer surface 114b includes a
corresponding electrode 110b that is modulated or energized to
attract charged species 106 from the heated air stream 104. The
corresponding electrode 110b may, for example, include a
conduction path within a conductive wall defined at least
partially by the heat transfer surface 114b. This may be
particularly appropriate when the wall is electrically isolated
and lies adjacent a substantially non-conductive heat sink, as in
an air-to-air heat exchanger for example. Alternatively, the
corresponding electrode 110b may overlie the heat transfer surface
114b, for example according to an embodiment corresponding to that
of FIG. 3. Alternatively, the corresponding electrode 110b may be
disposed near the heat transfer surface 114b. As will be
appreciated, while an electrode 110b disposed near the heat
transfer surface 114b may not drive the charged species 106 to
accelerate toward the heat transfer surface, it may impart
sufficient momentum to the charged species 106 (and any
non-charged or oppositely-charged species entrained therewith) to
cause them to impinge upon the heat transfer surface 114b as shown
diagrammatically.
[0074] Charged species 106 that impinge upon the heat transfer
surface 114b may do so by penetrating a boundary layer 602b. The
penetration of the charged species 106 may cause the boundary
layer 602b to be thinner than the boundary layer 602a. The
penetration of the charged species 106 may also effectively raise
the Reynolds number sufficiently to substantially convert a
laminar boundary layer 602a to a turbulent boundary layer 602b.
The mixing or disruption of the boundary layer 602b by the
impinging charged species, any entrained non-charged species, and
any entrained oppositely-charged species may result in raising a
heat transfer coefficient for transfer of heat from the heated gas
stream 104 through the heat transfer surface 114b.
[0075] Additionally, a combination of charged species 106 with
opposite charge carriers in the electrode 110b may release a heat
of association corresponding to a lower energy state of a neutral
species. Additionally, the kinetic energy of the charged species
106 (and other entrained species) impinging on the heat transfer
surface 114b may be converted to additional heat energy.
[0076] While the flame 102 and burner assembly 103 are depicted in
FIGS. 1, 2, and 5, as resembling a gas burner and flame, various
burner embodiments are contemplated. For example, the burner
assembly may include one or more of a fluidized bed, a grate,
moving grate, a pulverized coal nozzle, a gas burner, a gas
nozzle, an oil burner, arrays of burner assemblies, or other
embodiments. Flames 102 may include laminar flames, other
diffusion flames, premixed flames, turbulent flames, agitated
flames, stoichiometric flames, non-stoichiometric flames, or
combinations thereof.
[0000] Driving Heat Away from a Surface
[0077] While description above has focused on driving heat energy
toward a surface, other embodiments can drive heat energy away
from a surface. Generally, this can be accomplished by inverting
either the polarity of the highest concentration charged species
in the gas stream, by moving the location of the electrode(s) with
respect to the heat transfer (or temperature-sensitive)
surface(s), by inverting the voltage waveform applied to the
electrode(s), or by applying a (opposite sign) bias voltage to the
waveform. In most combustion systems, the highest mass and highest
stability charged species are positively charged. Therefore, for
most practical solutions involving combustion systems, the best
options may involve either moving the electrode(s), substantially
inverting the voltage waveform applied to the electrode(s), or by
applying or inverting a bias voltage to the voltage waveform.
[0078] FIG. 7 is a diagram of a system 701 configured to protect a
temperature-sensitive surface 702 and/or an underlying
temperature-sensitive structure 704 from heat transfer, according
to an embodiment. The operation of the system 701 may correspond
to the operation of the system 101 shown in FIG. 1, except that
the electric field or the charged species population is inverted.
[0079] The system 701 may typically include a flame 102 supported
by a burner assembly 103. A combustion reaction in the flame 102
generates a heated gas 104, that exhibits a mass a flow
illustrated by the arrow 105, carrying electrically charged
species 106, 108. Typically, the electrically charged species
include positively charged species 106 and negatively charged
species 108.
[0080] Providing a heated gas carrying charged species 106, 108
may include burning at least one fuel from a fuel source 118, the
combustion reaction providing at least a portion of the charged
species and combustion gasses. According to some embodiments, the
combustion reaction may provide substantially all the charged
species 106, 108.
[0081] The charged species 106, 108 may include unburned fuel;
intermediate radicals such as hydride, hydroperoxide, and hydroxyl
radicals; particulates and other ash; pyrolysis products; charged
gas molecules; and free electrons, for example. At various stages
of combustion, the mix of charged species 106, 108 may vary. As
will be discussed below, some embodiments may remove a portion of
the charged species 106 or 108 in a first portion of the heated
gas 104, leaving a charge imbalance in another portion of the
heated gas 104.
[0082] For example, one embodiment may remove a portion of
negative species 108 including substantially only electrons,
leaving a positive charge imbalance in the gas stream 104.
Positive species 106 may then be electrostatically attracted away
from the vicinity of a structure 704, resulting in reduced heat
transfer across a temperature-sensitive surface 702 of the
structure 704 and to the temperature-sensitive structure 704
itself. Alternatively, a portion of positive species 106 may be
removed from the heated gas stream 104, leaving a negative charge
imbalance in the gas stream. While the negative species 108 is
shown with a drift velocity toward the structure 704 and the
temperature-sensitive surface 702, the waveform applied to the
voltage source may, in fact, cause a net neutral path along the
mass flow 105 or may also drive the negatively charges species
away from the structure 704 with its temperature-sensitive
surface. This may be done by controlling modulation on-off cycles
and the duty cycle of the waveform in a manner corresponding to
the charge/mass ratio of the negative species 108. Alternatively,
with a low enough mass negative species 108 and/or depopulation of
the negative species 108, the negative species 108 may impart
negligible momentum upon the gas stream 104, and thus may not
result in substantial movement of heated gases toward the
structure 104 and temperature-sensitive surface 702.
[0083] A first electrode 110 may be voltage modulated by a voltage
source 112. The voltage modulation may be configured to create a
voltage potential across the heated gas stream 104 to drive a
portion of the charged species 106, here illustrated as positive,
away from the structure 704 and temperature-sensitive surface 702.
Modulating the first electrode may include driving the first
electrode to one or more voltages selected to, in combination with
a counter electrode 706, repel oppositely charged species, and the
repelled oppositely charged species imparting momentum transfer to
the heated gas.
[0084] The momentum from the electrically driven charged species
106 may be transferred to non-charged particles, unburned fuel,
ash, air, etc. carrying heat. The modulated first electrode 110
may be configured to repel the charged species and other entrained
species carrying heat to preferentially flow away from a
temperature-sensitive surface 702. As the heat-carrying species
flow away from to the heat transfer surface 114, a reduced portion
of the heat carried by the heated gas 105 is transferred through
the temperature-sensitive surface 702 to the structure 704.
[0085] According to an embodiment, the first electrode 110 may be
arranged near the temperature-sensitive surface 702. A nominal
mass flow 105 may be characterized by a velocity (including speed
and direction). The first electrode 110 may be configured to
impart a drift velocity to the charged species 106 at an angle to
the nominal mass flow velocity 105 and away from the
temperature-sensitive surface 702.
[0086] As mentioned above, the system 701 may further modulate at
least one second electrode 120 to remove a portion of the charged
species 106, 108. According to an embodiment, the second electrode
120 may preferentially purge negatively-charged species 108 from
the heated gas 104. According to an embodiment, the second
electrode may preferentially purge a portion of electrons 108 from
the heated gas 104.
[0087] According to an embodiment, the at least one second
electrode 120 may include a burner assembly 103 that supports a
flame 102, the flame 102 providing a locus for the combustion
reaction. The second electrode 120 may be driven with a waveform
from the voltage source 112. Alternatively, the second electrode
may be driven from another voltage source or may be held at
ground.
[0088] The counter electrode 706, which may be referred to as a
third electrode (whether or not the optional second electrode is
present), is shown as electrically coupled to ground. The third
electrode 706 may optionally be formed as a grounded combustion
system structure, and may thus not be an explicit structure.
Optionally, the third electrode 706 may be driven from the voltage
source 112 (via a connection that is not shown that replaces the
ground connection) or another voltage source (not shown) with a
waveform that is opposite in sign to the waveform applied to the
electrode 110.
[0089] Optionally, the electrode 110 may be combined with the
structure 704 or may be formed on the surface of the structure
704. For example, the first electrode 110 may be disposed over an
electrical insulator and the electrical insulator is disposed over
the temperature-sensitive surface 702 or the electrode 110 may be
formed from the structure 704 and/or the temperature-sensitive
surface 702. The electrical insulator may, for example, include at
least one of polyether-ether-ketone, polyimide, silicon dioxide,
silica glass, alumina, silicon, titanium dioxide, strontium
titanate, barium strontium titanate, or barium titanate. The first
electrode 110 may include at least one of graphite, chromium, an
alloy including chromium, an alloy including molybdenum, tungsten,
an alloy including tungsten, tantalum, an alloy including
tantalum, or niobium-doped strontium titanate.
[0090] The structure 704 and temperature-sensitive surface 702,
optional electrical insulator (not shown), and first electrode 110
may form at least a portion of a wall of a fire tube or water tube
boiler. In another example, the temperature-sensitive surface 702
and the structure 704 may include a turbine blade or other
structure subject to degradation by exposure to the hot gas stream
104. The temperature protection approaches shown herein may then
be used to extend turbine (or other structure) life, improve
reliability, reduce weight, and/or increase thrust by allowing
hotter combustion gases 104 without degrading the
temperature-sensitive structure(s) 704 and/or
temperature-sensitive surface(s) 702. The temperature-sensitive
surface 702 (and optionally structure 704) may include one or more
of titanium, a titanium alloy, aluminum, an aluminum alloy, steel,
stainless steel, a composite material, a fiberglass and epoxy
material, a Kevlar and epoxy material, or a carbon fiber and epoxy
material.
[0091] Optionally, the electrode 110 may be positioned away from
the structure 704 and temperature-sensitive surface 702 to
directly exert an attractive force on the majority species 106.
FIG. 8 is a diagram of a system configured to protect a
temperature-sensitive surface 702 and/or an underlying
temperature-sensitive structure 704 from heat transfer, according
to an embodiment where the electrode 110 is positioned distal from
the structure 704 and surface 702. The operation of the system 701
may correspond to the operation of the system 101 shown in FIG. 1,
except that the position of the electrode 110 is moved away from
the surface 702.
[0092] The system 801 may typically include a flame 102 supported
by a burner assembly 103. A combustion reaction in the flame 102
generates a heated gas 104, that exhibits a mass a flow
illustrated by the arrow 105, carrying electrically charged
species 106, 108. Typically, the electrically charged species
include positively charged species 106 and negatively charged
species 108. Operation of the combustion portion of the system 801
and the optional second electrode 120 may be substantially
identical to the operation of the system 701, as described above.
[0093] Positive species 106 and remaining negative species 108 may
then be electrostatically attracted away from the vicinity of the
structure 704, resulting in reduced heat transfer across a
temperature-sensitive surface 702 of the structure 704 and to the
temperature-sensitive structure 704 itself. Alternatively, a
portion of positive species 106 may be removed from the heated gas
stream 104, leaving a negative charge imbalance in the gas stream.
[0094] A first electrode 110 may be voltage modulated by a voltage
source 112. The voltage modulation may be configured to create a
voltage potential across the heated gas stream 104 to drive a
portion of the charged species 106, here illustrated as positive,
away from the structure 704 and temperature-sensitive surface 702.
Modulating the first electrode may include driving the first
electrode to one or more voltages selected to, in combination with
a counter electrode 706, attract oppositely charged species, with
the attracted oppositely charged species imparting momentum
transfer to the heated gas 104. As described above, while the
negative species 108 is shown with a drift velocity toward the
structure 704 and the temperature-sensitive surface 702, the
waveform applied to the voltage source may, in fact, cause a net
neutral path along the mass flow 105 or may also drive the
negatively charges species away from the structure 704 with its
temperature-sensitive surface 702.
[0095] The momentum from the electrically driven charged species
106 may be transferred to non-charged particles, unburned fuel,
ash, air, etc. carrying heat. The modulated first electrode 110
may be configured to attract the charged species and other
entrained species carrying heat to preferentially flow away from a
temperature-sensitive surface 702. As the heat-carrying species
flow away from to the heat-sensitive surface 702, a reduced
portion of the heat carried by the heated gas 105 is transferred
through the temperature-sensitive surface 702 to the structure
704.
[0096] A counter electrode 706, which may be referred to as a
third electrode (whether or not the optional second electrode is
present), is shown as electrically coupled to ground. The third
electrode 706 may optionally be formed as a grounded combustion
system structure, and may thus not be an explicit structure.
Optionally, the third electrode 706 may be driven from the voltage
source 112 (via a connection that is not shown that replaces the
ground connection) or another voltage source (not shown) with a
waveform that is opposite in sign to the waveform applied to the
electrode 110.
[0097] Optionally, the electrode 706 may be combined with the
structure 704 or may be formed on the surface of the structure
704. For example, the third electrode 706 may be disposed over an
electrical insulator and the electrical insulator is disposed over
the temperature-sensitive surface 702 or the third electrode 706
may be formed from the structure 704 and/or the
temperature-sensitive surface 702. The electrical insulator may,
for example, include at least one of polyether-ether-ketone,
polyimide, silicon dioxide, silica glass, alumina, silicon,
titanium dioxide, strontium titanate, barium strontium titanate,
or barium titanate. The third electrode 706 may include at least
one of graphite, chromium, an alloy including chromium, an alloy
including molybdenum, tungsten, an alloy including tungsten,
tantalum, an alloy including tantalum, or niobium-doped strontium
titanate.
[0098] The structure 704 and temperature-sensitive surface 702,
optional electrical insulator (not shown), and third electrode 706
may form at least a portion of a wall of a fire tube or water tube
boiler. In another example, the temperature-sensitive surface 702
and the structure 704 may include a turbine blade or other
structure subject to degradation by exposure to the hot gas stream
104. The temperature protection approaches shown herein may then
be used to extend turbine (or other structure) life, improve
reliability, reduce weight, and/or increase thrust by allowing
hotter combustion gases 104 without degrading the
temperature-sensitive structure(s) 704 and/or
temperature-sensitive surface(s) 702. The temperature-sensitive
surface 702 (and optionally structure 704) may include one or more
of titanium, a titanium alloy, aluminum, an aluminum alloy, steel,
stainless steel, a composite material, a fiberglass and epoxy
material, a Kevlar and epoxy material, or a carbon fiber and epoxy
material.
[0099] Optionally, the approaches related to heat attraction
(shown in FIG. 1 and elsewhere) may be combined with the
approaches related to heat protection (shown in FIGS. 7 and 8).
For example, the voltage source 112 may be configured to
preferentially apply heat to a heat sink 116 during a portion of a
cycle or for a period, and then preferentially remove heat from
the heat sink structure 704 during another portion of the cycle or
after the period is over. This may be used, for example, to
temporarily apply higher thrust against a turbine blade, such as
during periods of full military power, and then allow the turbine
blades to cool in order to avoid structural failure.
[0100] While the flame 102 in FIGS. 7 and 8 is illustrated in a
shape typical of a diffusion flame, other combustion reaction
distributions may be provided, depending upon a given embodiment.
[0101] Various configurations of embodiments depicted in FIGS. 7
and 8 are contemplated. For example, the first electrode 110
and/or the third electrode 706 may either or each include a
plurality of electrodes configured to impart drift velocities to
electrically charged species at a plurality of angles to the
nominal mass flow velocity. The first electrode 110 and/or the
third electrode 706 may include a plurality of first electrodes
110 and/or third electrodes 706, and the temperature-sensitive
surface 702 (and structure(s) 704) may include a plurality of
temperature-sensitive surfaces 702 (704). At least a portion of
the plurality of first electrodes 110 may then be interdigitated
with at least a portion of the plurality of temperature-sensitive
surfaces 702.
[0102] As indicated above, the voltage waveform provided by the
voltage source 112 may be driven as indicated elsewhere herein,
typically inverted or at an opposite bias for the arrangement 701
of FIG. 7, or directly as previously shown for the arrangement 801
of FIG. 8. The waveform may include a dc negative voltage, an ac
voltage including a negative portion, or an ac voltage on a dc
negative bias voltage for the arrangement of FIG. 8. Similarly,
the waveform may include a dc positive voltage, an ac voltage
including a positive portion, or an ac voltage on a dc positive
bias voltage for the arrangement of FIG. 7.