US3367415A

US3367415A - Anisotherm evaporation heattransfer structure

Info

Publication number: US3367415A
Application number: US512090A
Authority: US
Inventors: Charles A E Beurtheret
Original assignee: Compagnie Francaise Thomson Houston SA
Current assignee: Compagnie Francaise Thomson Houston SA
Priority date: 1964-12-17
Filing date: 1965-12-07
Publication date: 1968-02-06
Anticipated expiration: 1985-02-06
Also published as: GB1119518A; DE1501481B2; ES320596A1; BE673484A; DE1501481A1; IL24737A; FR1444696A; OA02050A; SE313585B; AT257543B; DE1501481C3; LU50058A1; CH519694A

Description

Feb. 6, 1968 ANISOTHERM EVAPORATION HEAT-TRANSFER STRUCTURE Filed Dec. '7, 1965 CD (with 1M M g; q 135 Q \l' 50 20 l 10 A N B a 0 w 100102 105 $10 120125 150 00|225 300 600 1100 1300 ts kn L c. A. E. BEURTHERET 3,367,415

5 Sheets-Sheet 1 Feb. 6, 1968 c. A. E. BEURTHERET 3,367,415

ANISOTHERM EVAPORATION HEATTRANSFER STRUCTURE 5 Sheets-Sheet 2 Filed Dec. 7, 1965 Feb. 6, 1968 I c. A. E. BEURTHERET 3,367,415

ANISOTHERM EVAPORATION HEAT-TRANSFER STRUCTURE Filed Dec. 7, 1965 5 Sheets-Sheet 5 Feb. 6, 1968 c. A. E. BEURTHERET 3,367,415

Filed Dec. 7, 1965 5 Sheets-Sheet 4 mmwmk 1968 c. A. E. BEURTHERET 3,

ANISOTHERM EVAPORATION HEAT-TRANSFER STRUCTURE Filed Dec. 7, 1965 5 Sheets-Sheet 5 United States Patent 3,367,415 ANISOTHERM EVAPORATION HEAT- TRANSFER STRUCTURE Charles A. E. Beurtheret, Saint-Germain-en-Laye, France,

assignor to Compagnie Francaise Thomson Houston- Hotchkiss Brandt, Paris, France, a corporation of France Filed Dec. 7, 1965, Ser. No. 512,090 Claims priority, application France, Dec. 17, 1964,

,075 11 Claims. (Cl. 165-185) ABSTRACT OF THE DISCLOSURE An anisotherm heat dissipating structure with generally trianguiar (in cross section) protuberances, so proportioned that at a near maximum nominal heat input rate, the protuberances operate to shoot off jets of vapor from their apices.

This invention relates to heat transfer structures of the type including a wall having one side exposed to a source of heat and its other side in contact with a vaporizable liquid into which the heat is dissipated. More especially, the invention relates to such structures that operate in a non-isotherm (or anisotherm) manner, as this term will be presently defined. Anisotherm evaporation heatdissipating structures are now widely used in many fields of engineering, including high-power electron tubes, evaporators, and other apparatus.

The general attractiveness of evaporation cooling methods as distinct from methods using a single-phase heattransfer fluid (liquid or gas), arises from the large amounts of heat absorbed by evaporation. However, such methods remained for many years an unattainable goal for high heat inputs because of the destructive phenomenon known as burn-out. This obstacle was first effectively overcome with the advent of the applicants so-called anisotherm eva oration structures in the 1950s. The burn-out effect and the manner in which it was mastered will briefly be described as a necessary preliminary to an understanding of the present invention.

Referring to FIG. 1 of the drawings, the graph 1 is well-known as the Nukiyama curve, and seeks to express the law of heat transfer between a wall made of heat conductive material and a boiling liquid (water at atmospheric pressure in the case of the graph shown). The ordinates represent the rate of heat transfer per unit area (otherwise stated heat flux density) in watts per square centimeter, and the abscissae represent surface temperatures in C. above saturation temperature t (100 C. in this instance). The curve has four main sections: a lowslope section A up to a knee point N, over which heat transfer is through normal convection, without the liquid boiling; a second steep-rising section B, from knee N to peak M, in which the water undergoes normal or socalled nucleate boiling, and the rate of heat transfer through convection is greatly increased; a third drooping section C from peak M to point L (known as the Leidenfrost point), which corresponds to a region of transition; and a fourth rising final section D from point L onwards, in which the vaporization of the water proceeds by socalled film-boiling (or spheroidal state) rather than the ordinary nucleate or bubble-boiling as at low surface temperatures.

The meaning of the graph is that, when any surface element is held at any strictly constant temperature selected on the abscissae axis, as by appropriately regulating the heat applied from the heat source to the wall, then the rate of heat dissipation remains generally constant Patented Feb. 6, 1968 at the corresponding ordinate value of the curve. In practice however, the heat source usually imposes the heat flux density through the wall and under these conditions it is found that the operating point first follows the first two rising sections A and B of the curve as far as the peak point M, and then, the operating point jumps from point M to a point Q positioned at a corresponding ordinate on the fourth section D, resulting in an increase in surface temperature as from about C. to more than 1000 C. usually causing irretrievable damage to the surface material. This enormous and sudden increase in the temperature of an element of the cooling surface is allowed to exceed at some point the comparatively mod erate temperature of the critical point M (125 C. in the case of boiling water at atmospheric pressure), constitutes the irreversible overheating effect known as burnout, and the critical point M on Nukiyamas curve has accordingly been known as the burn-out point. Wherever the heating rate from the source is so high as to cause the burn-out point to be locally exceeded in any portion of the cooling surface by even an exceedingly small amount, i.e. wherever a hot-spot is formed, destructive burn-out of the surface ensues.

For many years the only known technique for avoiding burn-out was to increase the rate of circulation and pressure of the cooling liquid, in an endeavour to maintain the operating point on the rising portion B of Nukiyamas curve for greater rates of heat supply, and thus prolong the state of normal nucleate ebullition and retard the onset of the unstable transitional conditions. This involved maintaining the heat exchange surface strictly isotherm, at a uniform temperature sufiiciently below that of the burn-out point M to provide an adequate safety margin against local hotspot formation and consequent burn-out. The resulting conditions were essentially unstable however, and drastically limited the power outputs that could be safely dealt with.

In 1950, the applicant discovered that contrary to earlier belief it was feasible to construct an evaporation heat-dissipating structure wherein there would be no liability to burn-out at temperatures exceeding the critical point on the Nukiyama curve. In contrast to the older approach which was to take elaborate precautions for maintaining isotherm conditions throughout the heatexchange surface with a uniform temperature well below that of said critical point, the new approach was to render the surface deliberately and thoroughly non-isotherm. Massive protuberances, such as bosses or ribs, were formed on the surface exposed to the boiling liquid, such that the temperature at the root or base of the bosses near the metal surface would be considerably higher than the critical point while the temperature at the tips of the protuberances projecting into the liquid remained substantially lower than the critical temperature. A continuous temperature gradient was thus deliberately created along the side surfaces of the protuberances. This continuous gradient encompassed the critical temperature from a temperature well below to a temperature well above it, over a wide range that extended continuously from cooler areas in which ordinary nucleate ebullition or bubble boiling prevails (arc B of the Nukiyama curve) through hot areas within the transitional region (arc C) and, if so desired, on to the initial part of the very hot areas in the film boiling region (are D). The temperature gradient was found to be effective in stabilizing the peak point M, and the ensuing transitional region ML, earlier reputed unstable. The operating point of the heat transfer process then smoothly followed a descending arc of the curve instead of tending to jump uncontrollably to the intolerably high temperatures of more than 1000 C. (such as represented by point Q) so soon as the temperature would anywhere locally approach the critical temperature of point M, as was the case in the older types of evaporationcooling structures based on the isotherm approach.

Non-isotherm cooling structures constructed in accordance with the above principles are now widely used for the cooling of the anodes in electronic transmitter tubes, and have virtually replaced all earlier types of cooling instrumentalities as regards transmitter tubes of the higher power ratings. Similar structures are now being applied on an experimental scale to the cooling of combustion engine cylinders and in other fields.

Of the several U.S. and foreign patents granted the applicant for the non-isotherm heat dissipating structures, especial reference is here made to U.S. Ser. No. 260,245 filed Feb. 21, 1963 (now Patent No. 3,235,004, Feb. 15, 1966). The patent discloses certain relationships between the dimensions of the protuberances and between those dimensions and the heat conductivity factor of the material of which the structure is made. When those relationships are adhered to, it is found that the stabilizing effect of the temperature gradient along the non-isotherm sidewalls of the protuberances is enhanced. This, as explained in that patent, is due chiefly to the fact that one of the two dimensional relationship taught by the patent states that the grooves or channels between adjacent protuberances must be relatively narrow and deep with respect to their width, thereby serving as radial vapor ejectors. The forcible expulsion of vapor radially out of the grooves leaves the full extent of the sidewalls of the grooves available for the liquid to form a more extensive temperature gradient thereover with a more potent stabilizing action.

The requirement of providing deep narrow slot-like grooves between the protuberances as taught by applicant earlier patent is in some cases undesirable. Machining costs are increased and, further, the limitations speci fied by that patent are in some cases inapplicable to smallsized structures. Further, the narrow slots tend to clog up with scale deposits unless a purified liquid is used. It is, therefore, one object of the present invention to provide non-isotherm heat-dissipating structures having performance characteristics at least as high as the structures of the applicants prior patent while being free from deep or narrow channels and attendant limitations. Another object is to provide non-isotherm cooling structureswhich shall be more precisely and scientifically prederminable as to their dimensional and other characteristics in view of the performance specifications of the final structure.

In the course of applicants more recent work in the field of anisotherm evaporation-coolers, a rather fundamental finding was made. It was experimentally established that under the non-isothermal conditions employed in applicants systems the true shape of the heat-transfer curve as a function of temperature departs significantly from the long-established shape of the Nukiyama curve in the transitional region extending from the critical point to the Leidenfrost point, as will be more fully disclosed later herein. An object of the present invention is to derive full benefit from certain possibilities afforded by this discovery as applied to a practical structure.

The invention will now be disclosed more fully with reference to the accompanying drawings, wherein:

FIG. 1 is a graph, previously referred to, showing both the standard Nukiyama curve and the partly modified curve established by the applicant for the transitional region under non-isotherm conditions when a high value of temperature gradient is involved;

FIGS. 2, 3 and 4 are enlarged sectional views of respective embodiments of the invention using different shape protuberances;

FIG. 5 is a stylized representation showing the pattern of liquid and vapor that tends to form adjacent the nonisotherm cooling structure of the present invention under operating conditions approaching maximum or nominal heat dissipation rate;

FIG. 5a is a similar representation of the vaporization attcrn resent in the narrow-channel structure of a P P 4 plicants earlier U.S. Patent No. 3,235,004 (Ser. No. 260,245).

FIG. 6 is a view in projection on a plane at right angles to that of FIGS. 2, 3 and 4, as indicated by the arrows VIVI in FIG. 3, but to a somewhat smaller scale, and illustrating a modification of the invention:

FIGS. 7 and 8 are views similar to FIGS. 2, 3 and 4 showing further modifications in the shape of the protuberances, usable according to the present invention.

Referring again to FIG. 1, it has recently been established by the applicant that the standard Nukiyama curve, shown at 1 in the figure and earlier referred to herein, does not hold, or is only partly true, in the case of the non-isotherm heat dissipating structures of the class to which this invention relates. The departure from the accepted theory affects the o-called transitional region from the critical point M to the Leidenfrost point L. Through experiments using large numbers of small temperature probes inserted into drill holes in the protuberances of the applicants non-isotherm cooling structures, especially structures of the type disclosed in the aboveidentified patent, it has been shown that in a system wherein all of the intermediate transitional temperatures simultaneously coexist as a continuous temperature gradient encompassing the critical temperature of point M, as is the case with these structures, the dissipated heat flux densities not only are stable but are consistently higher than the values given by the traditional Nukiyama curve, and that the actual heat flux density values define a curve of the shape indicated in dot-dash lines at MRL.

A full theoretical interpretation of this finding cannot yet be submitted. All that can be said for the moment is that the heightened fluX/ temperature curve MRL appears to represent the normal physical situation that obtains in a non-isotherm system having an extensive temperature gradient, provided a sufiiciently smooth continuity can be maintained between the adjacent areas of the non-isotherm surface in which the temperature ranges are on opposite sides of the critical temperature (M), that is, the area in which nucleate (or bubble) boiling obtains, and the area in which transitional (or semi-film) boiling obtains. In this view, the new curve MRL would represent an example of the over-all, complex vaporization conditions that are actually present in the case of a non-isotherm system, whereas the curve MUL which alone was recognized by earlier Workers, is a fictional curve that only can represent a series of flux measurements successively performed on an isotherm surface at a series of different temperatures, but has no true physical significance to the extent that the full set of its points considered simultaneously can at no time coexist in any real non-isothermal system unless the gradient of temperature along the surface is very low.

Whatever the theory, it is manifest that the newly found curve MRL would display two outstanding benefits over the standard curve MUL, provided said new curve can actually be established in a practical system. The first benefit, of course, is its stability, already emphasized above. The second benefit lies in the considerably heightened flux density values it would make possible throughout the temperature range involved and the corre-- sponding enhanced heat dissipating capacity of the resulting structures.

In accordance with the present invention it has been found that the total vaporization curve of the form MRL can elfectively and reliably be established in an anisotherm heat-dissipating structure without necessitating narrow grooves between the protuberances, provided each protuberance is so proportioned that, when the structure is operated at or near maximum nominal heatinput conditions, each protuberance is individually capable of supporting the requisite temperature drop along its sidewalls as generated by said nominal heat input, and is also capable of conducting all of said heat applied to its base, into the surrounding fluid.

Referring to FIG. 5 (more fully discussed later), this shows the vaporization pattern present in the structure of the invention under maximum heat input conditions. Each protuberance (here shown triangular in contour) is seen to be shooting out a jet of vapor 14 from its apex. This ever-present vapor jet continually breaks up the edge of the film vapor that would otherwise tend to seal off the area of transitional (semi-film) boiling from the adjacent area of nucleate boiling, on each side surface of the protuberance. The desired continuity between the two portions of the over-all temperature gradients on each side surface, a requisite for the establishment of the improved total vaporization curve MRL, is thus achieved.

FIG. 5a (essentially similar to FIG. 4 of the aboveidentified prior patent) shows the vaporization pattern of the narrow-groove structure under similar operating conditions. As described in detail in the prior patent, jets of vapor are ejected from the outer ends of the individual grooves.

It is to be noted that in both systems, the turbulence created by each vapor jet acts to break up the vapor films and thus establish continuity of the temperature gradient over each side surface, as required for the establishment of the improved total heat transfer curve MRL. In both systems, each side surface is wetted with liquid substantially throughout its length. The difference is that in the earlier structure (FIG. 5a) the opposite side surfaces of each narrow groove cooperate to create this turbulance, whereas in the structure of the invention (FIG. 5), it is the opposite surfaces of each protuberance which cooperate in creating the desired turbulence and thus achieve an equivalent result without having to rely on the provision of the undesirably narrow grooves between the protuberances.

The proportioning of the protuberances in accordance with the present invention, will now be described.

PEG. 2 of the drawings shows one form of heat dissipating structure with which the invention may be embodied. The structure generally designated 3 includes a generally flat metallic wall 5 having protuberances or bosses 4 integrally projecting from one of its sides. It will be understood that in operation, this embossed side of the structure, hereinafter termed the outer side, is immersed in a boiling liquid, e.g. water, and that heat to be dissipated is applied to the opposite, or inner side of the wall 5 the shape of which is not critical.

The protuberances 4 may be disposed in rows aligned along two mutually perpendicular directions of the structure, with similar contours and spacings as seen in both directions; or they may constitute elongated parallel ribs.

While the protuberances 4 may assume various sectional contours, some of which are later described, it is important that they be tapered over at least part of their length in order to promote the afore-mentioned ejection of vapor from the tips of the protuberances. As shown in FIG. 2, the protuberances have a compositely tapered, obelisk-like shape including a frusto-pyramidal base section of large taper angle, a longer frusto-pyramidal body part of smaller taper angle and an outer tip or apex in the form of a pyradim of large taper angle. The bases of the protuberances are substantially contiguous. This is greatly preferred according to the invention since as disclosed herein and in contrast with the prior patent it is the protuberances, not the grooves, that constitute the active vapor-ejecting elements. A spacing-apart of the protuberances at their bases would needlessly reduce the active surface area of effective heat dissipation and reduce the heat-dissipating capacity of the structure.

To ensure that, when operating under maximum (i.e. nominal) heat input conditions, the protuberances will perform as here desired to shoot out vapor from their apices and thereby achieve the desired continuous temperature gradient conditions on both sidewalls of each protuberances, it has been established that the tapered protuberances must be so dimensioned that, when operated under said nominal heat-input conditions:

(1) Each protuberance is long enough to allow the input heat flux applied to its base to generate the requisite temperature drop between the base and apex of the protuberance; and

(2) The total surface of the protuberance is large enough to allow all of said heat flux to be dissipated into the surrounding fluid.

This dual condition can be formulated mathematically as will now be established.

The first condition states that the length (b) of the protuberance must be great enough so that, when the maximum specified input heat flux density value to be dissipated, is applied to the base of the prouberance from the inner side of the wall 5, there will be sufficient space for the full desired temperature drop t t =0 to become established between the root 6 and apex 7 of the protuberance. This condition can be written as follows:

0 b is a;

where c is the conductivity factor of the material, and k is a safety factor, equal to or somewhat greater than unity (but not exceeding 2).

0, the temperature drop in operation, is selected in dependency on the nature of the material, the nature of the evaporating fluid and the pressure conditions. 0 should not be taken substantially less than the extent of the transitional range t t (see FIG. 1), in order to ensure that a sufliciently broad temperature gradient, a prerequisite for the proper operation of the non-isotherm evaporation-cooling system, is present. On the other hand, 0 cannot be taken substantially greater than (t t since otherwise the maximum temperature t in the metal at the base of the protuberances might rise to unnecessary heights. In the case where the liquid is water at atmospheric pressure, the two bounding values just indicated for 0 are C. and C. respectively, as will be evident from FIG. 1. Satisfactory results are still obtained however if the temperature drop 0 is taken as small as 50 C. (with water at ordinary atmospheric pressure). Where the evaporating liquid is pressurized, and/Or is other than water, the temperature drop 0 may take values outside the just-indicated range of 80-125 C., as will be later indicated.

The second condition is derived from a consideration of the Laplace law of flux conservation through the protuberance.

The total amount of heat entering the base 9 of the protuberance, as indicated by arrow 10, must equal the total amount of heat issuing from the outer lateral surfaces of the protuberance, arrow 8, into the surrounding boiling liquid, per unit time. The total amount of heat entering the base of the protuberance is s where s is the area of the base 9. The total amount of heat leaving the outer side surfaces of the protuberance is s t where s is the total area of the side surfaces of the protuberance, and (p is the outgoing heat flux density, or mean rate of heat outflow referred to unit area of the protuberance side surfaces. The quantity ga will be more fully defined presently. Thus, the second condition must state that the side surface area s is large enough to provide for a complete outflow of heat at the rate (p therethrough in the presence of heat at the specified, nominalf rate through the base surface area s of the protuberance. This can clearly be written as The outgoing heat flux value (p appears in the graph of FIG. 1 as the mean value of flux density averaged over the temperature range t t of interest, under the modi- 2 -a a (curve MRI.)

In practice, and in the absenceof a convenient method of computing (p in terms of the temperatures 2 and 1 it is found satisfactory to express in terms of the flux density value q corresponding to Nukiyamas critical point M, and write where p is a numerical coefficient within the range from 0.8 to 1.6, (generally approximating unity), later discussed in greater detail, while q the critical flux density depends on the nature and pressure of the liquid used and can be found in standard works of reference (q=l35 w./cm. for water at atmospheric pressure).

The above second condition then becomes It is to be noted that the values of b, s,,, s 0, 0, and q in Equations I and II can be expressed in units selected among any coherent system of measures and weights, whatever are the bases of the units.

It will be understood that Equations I and II would, under ideal conditions, be taken with the coeflicient k equal to unity. That k is generally taken greater than 1 merely expresses a safety consideration, to allow for such uncertain contingencies as imperfect surface of the structure, possible occurrence of overloads in use, and the like. Making k greater than 1 means that the protuberances are built somewhat larger than would be strictly necessary under ideal conditions, thereby improving operating safety (but not efficiency). An upper limit for the safety factor k is set essentially by structural and economical considerations, and it is found in practice that such upper limit can conveniently be taken as two. Increasing the protuberance length b and area ratio s /s beyond twice their theoretical minima would not only be pointless in that it would not improve the heat dissipating capacity of the structure, but would lead to an uneconomical structure and increase the temperature t A simple and advantageous embodiment of the invention is shown in FIG. 3, where the protuberances have a triangular contour in section, with adjoining bases. Here again, the protuberances may be square-base pyramids disposed in rows aligned along two e.g. orthogonal directions of the wall surface, or they may be (and this is preferred) formed as elongated prismatic ribs extending in parallel relation over the wall surface.

The second above relation (II) can then be written in a somewhat more specific form. Using the dimensional notations indicated in FIG. 3, it is evident that s a sin a b 2. asina pq Sin can conveniently be equated with unity since the area ratio .q/s is relatively large in a high-performance structure and the angle is of the order of 60. Such approximation simply amounts to modifying somewhat the safety factor applied. The resulting simplified equation is then:

It will be understood that the relationships of the invention, (I) and (II), or (I) and (III), can alternativelybe written as independent inequations specifying operative ranges for the dimensional variables b and s /s or b and a. Thus, it is evident that relation (1) can be reformulated and, if b is eliminated between Equations I and III, the latter relation can be rewritten as the inequation 0.s fsas1.6

These relations provide a convenient means of determining the height I) and pitch 2a of the triangular protuberances required for any set of specified conditions.

It is noted that in the case of the triangular contour shown in FIG. 3, and if the protuberances are prismatic ribs as indicated above, the discharge heat flux density =pq is assumed to be uniform over the length 1 of the rib sides, and consequently also the temperature gradient is substantially uniform along the sides. The flux lines, such as 11, of the input heat applied to the base of the triangle are uniformly distributed over the inclined sides of the ribs, and the temperature along each side decreases linearly from 1 to t This uniform temperature distribution is considered desirable and the corresponding gen- (III) erally triangular contour is accordingly a preferred em-,

bodiment of the invention.

For constructional reasons, however, it is desirable to round off the corners at the base and tip of the protuberances, as shown in FIG. 4. The dimensional relationships disclosed herein should then be present when referred to the contour, shown in dash lines, defined by the centers of

curvatures

12 and 13 of the rounded arcs at the base and apex of the protuberance. The rounding-off of the corners reduces the areas over which the desired temperature gradients can be distributed. However, since the b dimension entering into the relations set forth above is measured between the curvature centers 12 and 13, it is evident from FIG. 4 that the effective height of the protuberance is somewhat increased over the theoretical value, and this increase in the effective length of the protuberance effectively compensates for the loss in surface area and provides the necessary space for the temperature gradient to extend over, despite the rounding-off of the corners.

The manner of operation of the heat-dissipating protuberances of the invention will now be discussed in greater detail with reference to FIG. 5. In the nominal operating conditions corresponding to or approaching the maximum specified heat output, the base and apex of each protuberance are at the temperature t and t respectively, with (t t ):6, since the protuberances are proportioned to ensure that this condition is present in accordance with relation (I) of the invention. The apex temperature i is somewhat below the temperature of critical point M (FIG. 1), since the temperature drop 0 was predetermined so that this should be true. The apex temperature t therefore, lies in the region B of nucleate or bubble boiling, preferably near the upper limit of this region, where the vapor nuclei tend to coalesce into large bubbles, the socalled coalescence range. Since this holds for both side surfaces of the protuberance on opposite sides from the apex thereof, and in view of the tapered shape of the protuberance, there results a situation in which the large steam bubbles generated. at the upper ends of both sidewalls of the protuberance combine into a common column of vapor 14 which is forcibly ejected from the apex of the protuberance. The columns 14 of intense vaporization 9 ejected from the protuberances act to bore holes, as it were, in the body of the surrounding liquid.

At the same time, each inclined side surface of the protuberance carries a stable temperature gradient from the root temperature t (generally approximating the Leidenfrost point t;,) to the apex temperature 1 (somewhat below the critical temperature t Thus, as indicated for one of the protuberance side surfaces in FIG. 5, a major region of each side surface is exposed to the transitional or semi-film boiling conditions designated as C in FIG. 1, and a minor region of the side surface towards the apex thereof is exposed to the coalescent bubble boiling conditions designated B. The junction of the two regions corresponds in temperature with that of the critical point M, as indicated.

The intense turbulence locally created by abovementioned column of vapor 14 in the upper portion of the side surface, contributes to the continued maintenance of the stable temperature gradient in that it continually breaks up the edge of the vapor film that would otherwise tend to form at the critical point M, at the separation between the transitional boiling region C and the nucleate boiling region B. Thus, the desired continuity between the two regions, earlier indicated as being a requisite for the continued existence of a stable temperature gradient, is accomplished.

What physically happens at point M, is that the constant break-up of the incipient vapor film-edge at this point provides a path of escape for the vapor film 15 in the transitional region C outwards through the nucleate boiling region B and to the hole constituted by the vapor column 14. The vapor film 15 in region C is thus continually deflated, and does not impair the intimate contact between the liquid phase 16 and the metal surface 17 of the protuberance. The conditions are thus present, which were earlier described herein as necessary and suflicient to ensure that the heightened heat-transfer curve MRL (FIG. 1) is followed, with the attendant advantages of stability and boosted heat-transfer efficiency.

A comparison between FIG. and FIG. 5a (which coresponds to FIG. 4 of the earlier US. Patent 3,235,004) is of interest in that it makes evident both the similarity and the diiferenecs between that earlier patent and the present invention. In both cases, stable temperature gradients are present throughout the extent of the walls of the heatdissipating formations. Each sidewall has a continuous set of points encompassing both types of boiling to either side of the critical temperature at point M. In both cases therefore, heat transfer from the metal to the fluid takes place in accordance with the boosted, socalled total heat transfer curve MRL. Also, in both cases a substantially uniform wetting of the wall surfaces with liquid is present, without cluttering of the interprotuberance channels with vapor. However, in the earlier patent application these conditions are achieved as the result of an ejection of steam from the outer ends or mouths of the inter-protuberance grooves or channels, and accompanying turbulence produced by interaction between the two side surfaces of common channel. In the present invention, an essentially equivalent situation is provided as the result of steam ejection from the apices of the protuberances, and accompanying turbulence produced by interaction between the side surfaces of a Common protuberance.

Hence, in the present case it is the proportioning of the protuberances not the grooves that is critical, and narrow slot-like grooves need no longer be used.

Elimination of the narrow slot-like channels or grooves between the protuberances not only facilitates machining and makes the structure easier to embody in small sizes. It also facilitates the fluid circulation. As described in said earlier patent, the fluid circulation associated with the operation of the narrow grooved structure there disclosed involves a radial outflow of vapor from the outer ends or mouths of the channels and a simultaneous axial inflow of liquid from a longitudinal end of the channels. In the structure of this invention, the fluid circulation tends to assume a different pattern. This pattern involves a radial outflow of vapor from the apices of the protuberances and a simultaneous radial inflow of liquid through the outer radial ends of the channels between the protuberances (as indicated by arrows 30). Such a pattern still ensures a smooth fluid circulation with distinct and separate paths for the inflow of liquid and discharge of vapor, avoiding a clutter of large vapor bubbles in the bottoms of the channels which would interfere with the feed of liquid thereinto, as tended to be the case with applicants earlier non-isotherm cooling structures prior to the aforementioned patent.

Because of the substantial absence of axial liquid flow in the channels in the structure of the invention, it generally becomes less important to provide for transverse recesses for the intake of liquid into the channels as was required in the prior patent, and the protuberances may be provided in the form of continuous ribs extending the full axial length of the structure. In some cases however, the provision of such transverse channels is found beneficial in that it promotes turbulence while reducing the weight of the structure. As shown in FIG. 6, the ribs like protuberances 4, having a transverse contour of the type described above with reference to FIG. 3 or 4, are interrupted with longitudinally-spaced, transversely-extending recesses 19. Where the spacing d between these transverse channels or recesses does not greatly exceed the base width 2a of the protuberances in the transverse direction (FIGS. 3 or 4), the transverse channels 19 are preferably V-shaped as shown, with the angle a being the same as that shown in FIG. 3.

As disclosed in another of applicants US. patents relating to non-isotherm evaporation-cooling structures, U.S. Patent 3,299,949, Jan. 24, 1967, it has been found advantageous in many cases to increase the heat dissipating capacity of terminal portions of the protuberances in such structures as compared to the main body portion of the protuberance. This refinement may be applied to the structures of the present invention, as shown by way of example in FIGS. 7 and 8. In FIG. 7, the protuberance 4 is generally triangular in contour and proportioned as earlier disclosed herein. However, the apical part of the protuberance has

castellations

20, 21 formed therein by means of cuts spaced along the length of the riblike protuberance and extending from the top thereof, and preferably these castellations are alternately bent in opposite directions. This, as explained in the last-mentioned patent, increases the heat-dissipating area near the top of the protuberance and tends to lower the temperature at the apex, improving the stability of the temperature gradient. In FIG. 8, a generally similar result is obtained by providin an outer part 24 of the protuberance 4 of constant width instead of tapered. The uniformwidth outer portion 24 should have a width less than half the base width 2a of the protuberance, so that the protuberance will still remain tapered over a major part of its length as prescribed in accordance with this invention. It is found that in such conditions the relatively enlarged outer portion 24 does not interfere with the satisfactory ejection of vapor from the apex (preferably castellated) of the protuberance as explained with reference to FIG. 5. Instead of or in addition to the arrangements shown in FIGS. 7 and 8, the surfaces of the outer part of the protuberance may be roughened further to increase the relative heat dissipating area thereon, and/or other of the expedients disclosed for a similar purpose in the lastmentioned patent may be applied. When the heat-dissi' pating area is increased in the terminal part of the protuberances, as just described, the safety factor k is preferably taken rather large, e.g. from 1.5 to 2.

Some additional data will now be given concerning the parameters entering into the relationships of the invention. The factor p is equal to the ratio p q of the heat output flux density actually present in the device to the mean critical flux density as derived from Nukiyamas curve. (The critical flux density q as earlier noted is determinable for any particular fluid and under any particular pressure conditions from available tabulations, or by formulas such as Kutadeladzes formula.) The factor p is in the nature of an efiiciency factor. It can generally be taken equal to unity, when the upper temperature value t at the base of the protuberances is near the Leidenfrost point, but is preferably taken slightly less than unity (say 0.8 or 0.9) if said maximum temperature t is greater than the Leidenfrost temperature 11,. In cases where the temperature gradient 19/!) set up along the protuberance sidewalls in operation is relatively great (say greater than about 200 C./centimeter), it is found that the efficiency factor p can actually be taken greater than 1, and can attain the surprisingly high value of 1.5 or 1.6. However, a preferred range for the efliciency factor p is from 0.8 to 1.2. It will be understood that this range of deviation of the efficiency factor from its usual value of 1, is a consequence of the fact that the true output flux density (p is actually a function of the temperature drop t t =6, as indicated by the integral Equation 3, rather than being a constant as assumed for convenience in the relationships used in practicing the invention.

In determining the operational temperature drop =t t the lower or apex temperature t can usually be considered as equal to the saturation temperature t of the cooling fluid at the pressure used, e.g. t :100 C. in the case of water at atmospheric pressure, so that 0=r r The higher or base temperature t should, as will be understood from earlier explanations, approach the Leidenfrost point temperature t (225 C. for water at ordinary pressure). If t is taken too high above the Leidenfrost point the average value of will decrease. Generally, the temperature drop 0 will be in a range of from 50 C. to 150 C. For water at ordinary pressure, a preferred range for 0 is from 80 to 120 C.

The invention makes it possible successfully to dissipate heat input rates substantially higher than the rates that can be dealt with by means of conventional structures, including values of exceeding the remarkably high value of 1000 watts per square centimeter. While the use of the invention is also contemplated in connection with moderate and low heat output rates, except in certain special applications some of which will be indicated later, it is generally regarded as of minor interest to use the improved structures as coolers in cases where the heat rate to be dissipated does not exceed, say, 200 watts/sq. cm. In terms of the critical flux density q, it can be stated that the invention is useful in cooling applications with input heat flux densities (p in ,a range of from 1.5q to 6g. It will be understood that for the larger heat input rates, the value of q is preferably increased through an increase in the pressure applied to the fluid.

The evaporating liquid medium may be provided as a generally stagnant body in an enclosure surrounding the heat dissipating structure, so that its circulation will occur by the action of natural convection; or means may be provided for inducing a forced circulation of the fluid. In the case of large structures and high heat input rates, forced circulation of the liquid (together with preferably increase pressure) is advantageously used, at a suificient flow rate to condense a major part of the vapor formed adjacent the structure. The ready inflow of the liquid radially into the inter-protuberance channels, as described earlier herein, is thereby facilitated.

Practical examples including specific numerical data for the improved evaporation structures will now be described Example 1 In a moderate-power cooling structure for a diesel engine, it was desired to dissipate a heat input flux density of =250 watts per sq. cm., using a cast iron wall structure, with naturally-circulating water at atmospheric 12 pressure as the evaporating medium. Using rib-like protuberances of triangular prismatic contour as in FIG. 3, a temperature drop 0:100" C. and an efficiency factor p=l, and noting that the heat conductivity of cast iron is c=-0.5 w./cm. C., application of Equations I and II or III gives the following results for a safety factor k=1.5:

12:0.3 cm. and 2a=0.22 cm.

If the factor sin or is concerned it is seen that the pitch 2a may be increased to 0.25 cm.

Example 2 In a cooling apparatus for a high-power vacuum tube having a total power rating of 170 kw. and an anode area of 155 cmF, it was necessary to dissipate 1100 watts/ sq. cm. over a large area. A copper heat dissipating structure (c=3.7 w./cm. C.) was used, with forced circulation of water at 3.5 atmosphere pressure. Rib-like protuberances of generally triangular sectional contour were 150 1,100 Since it is contemplated that the apparatus shall be capable of taking considerable instantaneous overloads in service, the safety factor k is in this example taken equal to 2. The length of the protuberances is accordingly taken equal to b=0.5 2=1 centimeter.

At the pressure used for the evaporation medium (3.5 atm.), the critical flux density q for water is found (e.g. from the well-known Kutadeladze formula) to be q=300 w./crr1. C. The efliciency factor p is in this instance selected near the upper limit of its range, because of the high temperature gradient applied and the favourable effect of the condensation by a flow of subcooled water. Thus, p was made equal to 1.5. Equation III then provides a value 211:0.37 centimeter, for the root width of the protuberances.

Tests have shown the structure constructed in accordance with this example to be fully capable of dissipating the specified power input under steady-state conditions, and of satisfactorily taking up momentary overloads in a reliable manner, this being permitted by the large value of the safety factor k=2. The performance characteristics of this structure will be seen to be especially remarkable, in the light of cooling structures of the prior art, in that the heat resistance thereof is as low as 0.2 C. cmF/watt at a nominal heat flux density higher than 1 kw./cm. and using a water circulation at a relatively low flow rate (less than 0.5 liter/minute per kilowatt dissipated power), and under the limited pressure indicated above (3.5 atm.). An additional practical advantage the structure is found to possess is its self-cleaning action whereby it will spontaneously eliminate incrustations that otherwise end to form in the presence of hard feed water.

Other examples Heat dissipating structures according to the invention are applicable over wide ranges of conditions and the protuberances or teeth thereof can correspondingly assume widely differing proportions. Thus, with poorly conductive metals such as stainless steel (c=0.2 w./cm. C.), the b dimension will be less than 0.1 cm. for temperature drops 0 in the preferred range and nominal flux density 5 on the order of 500 w. per square centimeter of the heat input surface. Such structures are useful e.g. in steam generators, using boiling water at high pressure, e.g. atmospheres, having a saturation temperature z of 285 C.

Structures according to the invention are also usable in chemical processes as evaporators for liquids (e.g. chlorine trifluoride) having low chemical stability and poor heat transfer properties, including a very low critical flux densty q, and consequently requiring very low temperature drops 6 to be used, e.g. :20" C. Stainless steel evaporators for such purposes can be constructed according to the invention for operation at a heat transfer rate of 10 w./cm. using a protuberance length b of 0.5 cm.

It will be understood that when operating at low heat input conditions, as in this last example, relationship (I) assumes primary importance, while relation (II) or (III) becomes relatively uncritical.

In the general case however, and especially in the higher power ranges which are particularly contemplated by the present invention, the relationships taught herein are highly critical. Unless the ranges derived from these relationships are adhered to, it is found that the high heat dissipating performance referred to herein are not achieved.

It may be of interest to point out that elimination of the nominal flux density 5 between the relationships (I) and (III) of this invention provides the equation which is similar in form to the equation b=m /ac taught in the applicants earlier patent application (U.S. Ser. No. 260,245 filed Feb. 21, 1963) mentioned above. This equation is seen to be generic in character in that it governs the operation of all applicants non-isotherm evaporation heat-transfer structures, whether or not they conform With the present invention. It will, however, be evident that the relations of the present invention (I), (II) and (III) cannot be inferred from a consideration of this broad earlier-given equation alone.

Summarizing the present invention, this is based on the applicants discovery that the transfer between a surface and a boiling liquid will, under proper circum stances, follow a heat transfer law that departs significantly from the classical law represented by the Nukiyama curve in the so-called transitional region. The new law is advantageous in that it is both stable and involves higher rates of heat transfer. The invention provides anisotherm heat dissipating structures wherein the protuberances are so proportioned that, at and near the maximum nominal heat input rates the protuberances operate to shoot ofi jets of vapor from their apices. When this type of operation prevails, the advantageous newly discovered law of heat transfer becomes effective over the Walls of each protuberance. Heat dissipation is more efficient and operation more reliable.

What I claim is:

1. In a non-isotherm heat dissipating structure of the type comprising a wall of heat conductive material having one side exposed to a heat source and its opposite side exposed to a vaporizable liquid and formed with protuberances adapted in operation to have substantial temperature gradients established over the side-walls thereof, the improvement characterized in that the protuberances have adjoining bases and have sidewalls that are tapered over at least a substantial part of their length, and are so proportioned as to satisfy the relations:

wherein: b, s, and s are the length, base area and total side surface area, respectively, of a protuberance; c is the heat conductivity of said material; q is the critical flux density of heat transfer of the boiling liquid at the pressure of operation; 0 is the specified temperature drop from the base to the apex of a protuberance in operation;

4 is the nominal maximum heat flux to be applied to said side exposed to a heat source;

k is a numerical safety factor selectable within the range from 1 to 2; and

p is a numerical efficiency factor selectable within the range from 0.8 to 1.6, the values of b, s,,, s 0, 0, as and q being expressed in units of any coherent system of measures.

2. In an anisotherm heat dissipating structure of the type comprising a wall of heat conductive material having one side exposed to a heat source and its opposite side exposed to a vaporizable liquid and formed with protuberances adapted in operation to have substantial temperature gradients established over the sidewalls thereof, the improvement characterized in that the protuberances have a generally triangular contour as seen on a plane normal to said wall, with adjoining bases, and are so proportioned as to satisfy the relations:

wherein: Z) and a are the altitude, and half base width,

respectively, of the triangular contour;

c is the heat conductivity of said material;

q is the critical flux density of heat transfer of the boilin-g liquid at the pressure of operation;

0 is the specified temperature drop from the base to the apex of a protuberance in operation;

( 5 is the nominal maximum heat flux to be applied to said side exposed to a heat source the values of a, b, c, 0, and q being expressed in units of any coherent system of measures.

3. A structure according to claim 1, wherein the protuberances are elongated parallel ribs of uniform transverse contour.

4. A structure according to claim 1, wherein the protuberances are in the general form of pyramids aligned in two mutually orthogonal directions.

5. A structure according to claim 2, wherein the protuberances have rounded bases and apices, and wherein said relations are applied to the contour defined by the centers of curvature of said rounded bases and apices.

6. A structure according to claim 3, wherein said ribs are formed with parallel cutouts spaced along their length and perpendicular to the direction of the ribs.

7. A structure according to claim 1, wherein the protuberances are formed, over an outer end part thereof not exceeding one half their length, with means for increasing the contact surface area thereof with said liquid.

8. A structure according to claim 1, wherein said temperature drop 0 ranges from a temperature below the critical temperature t of the liquid to a temperature approximating that of the Leidenfrost point.

9. A structure according to claim 1, wherein said temperature drop is in the range from 50 C. to 150 C.

10. A structure according to claim 9, wherein the liquid is water at ordinary pressure and said temperature drop is in the range from to C.

11. A structure according to claim 1, wherein said nominal heat flux density is in the range from 1.5 to 6 times the critical flux density q.

References Cited UNITED STATES PATENTS 5/1960 Beurtheret 74 1/1961 Beurtheret 165-80