Measurements and modeling of deposition rates from near-supercritical, aqueous, sodium sulfate and potassium sulfate solutions to a heated cylinder

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 365-373).In the Supercritical Water Oxidation (SCWO) process, a technology emerging for the disposal of hazardous organic wastes, organic compounds containing heteroatoms such as S, Cl and P are oxidized to the corresponding acid. In order to reduce corrosion, bases are therefore often injected into the reactor. The salts that are formed upon neutralization (sulfates, chlorides, phosphates, etc.) have low solubility in supercritical water (SCW) and consequently precipitate as solid phases. These salts can form agglomerates and coat internal surfaces, leading to plugging of transport lines and inhibition of heat transfer. The purpose of this dissertation is to develop an understanding of salt deposition kinetics and nucleation phenomena at conditions relevant to SCWO. Solubility and deposition experiments were performed with aqueous sodium sulfate and aqueous potassium sulfate solutions at elevated temperatures and pressures typical of the SCWO process. For both the solubility and deposition experiments, the test cell is a six-port chamber which was fabricated by modifying a 1.91 cm (3/4 inch) diameter Swagelok cross. One port was used to mount a 0.200 inch (5.08 mm) diameter internally heated cylinder into the center of the chamber and the remaining ports provided fluid cross flow, visual observation capability and instrumentation access. Aqueous salt solutions containing up to 10 wt% salt were pumped at about 250 bar through preheaters that brought the solution to a temperature close to that at which precipitation occurs. Inside the test cell, the heated cylinder raised the temperature of the nearby solution above this precipitation temperature, thus limiting deposition almost exclusively to the heated cylinder. Experimental deposition rate data from sodium sulfate- and potassium sulfate-containing SCW streams to the heated cylinder were obtained by removing the heated cylinder from the cell following each run and measuring the mass of salt deposited on it. The deposition rate data were obtained as a function of time and concentration of salt in the solution entering the test cell. Salt concentration and time in the deposition experiments were varied between 2 and 8 wt% and 6 and 12 minutes respectively. In the solubility experiments, the solubility temperature of sodium sulfate and potassium sulfate in water at a pressure of 250 bar was measured for salt concentrations up to 10 wt%. Natural convection dominates transport at all of the conditions investigated in the solubility and deposition rate experiments. The equations governing the transport of salt to the interface that develops between the salt layer which forms on the heated cylinder/hot finger and the solution in the adjoining boundary layer are developed in a fairly rigorous context. Then, the equations governing transport are scaled to determine a set of criteria which, when satisfied or partially satisfied, allows various terms, e.g., those accounting for the Soret effect and Dufour effect in the species and energy conservation equations respectively, to be neglected or simplified. All of the criteria are evaluated for the conditions in the deposition experiments, justifying a relatively simple set of ordinary differential equations which govern the deposition rate of salt at the salt layer-solution interface. The simplified model is numerically solved to predict the rate of transport of salt to the salt layersolution interface for all the conditions investigated in the deposition experiments as a function of time. The theoretical deposition rate predictions are then compared to the deposition rate data in the context of a sensitivity analysis. For the deposition experiments in which the sodium sulfate and potassium sulfate concentrations in the solution entering the test cell were 4 wt% or less, the theory and data compare well. In fact most, but not all, of the experimental data for these experiments fall within the bounds predicted by a sensitivity analysis accounting for uncertainties in thermophysical properties and experimentally measured variables input into the theoretical deposition rate formulation. For higher salt concentrations, however, the model underpredicts the experimental data by up to a factor of about two. It is shown that, as the concentration of salt in the solution entering the test cell increases, deposition of salt within the porous salt layer formed on the hot finger is likely to become more significant. Thus it is hypothesized that the theory and deposition data do not compare as well at higher salt concentrations because the predictive model accounts for deposition at the salt layer-solution interface, but not deposition within the porous salt layer. In the model developed for the deposition rate of salt at the salt layer-solution interface it is assumed that salt nucleation occurs exclusively at the salt layer-solution interface, i.e., there is no homogeneous nucleation of salt in the boundary layer. This assumption is validated, to some extent, by visual observations during the experiments. Additionally, a major chapter of this dissertation is devoted to nucleation modeling. A model to predict whether or not homogeneous nucleation and/or supersaturation will occur in the boundary layer formed around the salt layer-solution interface is developed. It predicts that homogeneous nucleation and/or supersaturation are unlikely, if not impossible, at the conditions investigated in the deposition experiments. This justifies the formulation used to solve for the rate of mass transfer at the salt layer-solution interface a posteriori.by Mark S. Hodes.Ph.D

Asymptotic Nusselt numbers for internal flow in the Cassie state

We consider laminar, fully-developed, Poiseuille flows of liquid in the Cassie state through diabatic, parallel-plate microchannels symmetrically textured with isoflux ridges. Through the use of matched asymptotic expansions we analytically develop expressions for (apparent hydrodynamic) slip lengths and variously-defined Nusselt numbers. Our small parameter ($\epsilon$) is the pitch of the ridges divided by the height of the microchannel. When the ridges are oriented parallel to the flow, we quantify the error in the Nusselt number expressions in the literature and provide a new closed-form result. The latter is accurate to $O\left(\epsilon^2\right)$ and valid for any solid (ridge) fraction, whereas those in the current literature are accurate to $O\left(\epsilon^1\right)$ and breakdown in the important limit when solid fraction approaches zero. When the ridges are oriented transverse to the (periodically fully-developed) flow, the error associated with neglecting inertial effects in the slip length is shown to be $O\left(\epsilon^3\mathrm{Re}\right)$, where $\mathrm{Re}$ is the channel-scale Reynolds number based on its hydraulic diameter. The corresponding Nusselt number expressions are new and their accuracy is shown to be dependent on Reynolds number, Peclet number and Prandtl number in addition to $\epsilon$. Manipulating the solution to the inner temperature problem encountered in the vicinity of the ridges shows that classic results for thermal spreading resistance are better expressed in terms of polylogarithm functions.Comment: 41 pages, submitted to Journal of Fluid Mechanic

Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip

We semi-analytically capture the effects of evaporation and condensation at menisci on apparent thermal slip lengths for liquids suspended in the Cassie state on ridge-type structured surfaces using a conformal map and convolution. An isoflux boundary condition is prescribed at solid-liquid interfaces and a constant heat transfer coefficient or isothermal one at menisci. We assume that the gaps between ridges, where the vapor phase resides, are closed systems; therefore, the net rates of heat and mass transfer across menisci are zero. The reduction in apparent thermal slip length due to evaporation and condensation relative to the limiting case of an adiabatic meniscus as a function of solid fraction and interfacial heat transfer coefficient is quantified in a single plot. The semianalytical solution method is verified by numerical simulation. Results suggest that interfacial evaporation and condensation need to be considered in the design of microchannels lined with structured surfaces for direct liquid cooling of electronics applications and a quantitative means to do so is elucidated. The result is a decrease in thermal resistance relative to the predictions of existing analyses which neglect them

Living with the Past: Nutritional Stress in Juvenile Males Has Immediate Effects on their Plumage Ornaments and on Adult Attractiveness in Zebra Finches

The environmental conditions individuals experience during early development are well known to have fundamental effects on a variety of fitness-relevant traits. Although it is evident that the earliest developmental stages have large effects on fitness, other developmental stages, such as the period when secondary sexual characters develop, might also exert a profound effect on fitness components. Here we show experimentally in male zebra finches, Taeniopygia guttata, that nutritional conditions during this later period have immediate effects on male plumage ornaments and on their attractiveness as adults. Males that had received high quality food during the second month of life, a period when secondary sexual characteristics develop, were significantly more attractive as adults in mate choice tests than siblings supplied with standard food during this period. Preferred males that had experienced better nutritional conditions had larger orange cheek patches when nutritional treatments ended than did unpreferred males. Sexual plumage ornaments of young males thus are honest indicators of nutritional conditions during this period. The mate choice tests with adult birds indicate that nutritional conditions during the period of song learning, brain and gonad development, and moult into adult plumage have persisting effects on male attractiveness. This suggests that the developmental period following nutritional dependence from the parents is just as important in affecting adult attractiveness as are much earlier developmental periods. These findings thus contribute to understanding the origin and consequences of environmentally determined fitness components

Advanced Heat Sinks Enabled by Three-Dimensional Printing

With the rapid rise in power dissipated by integrated circuits, improved heat sinks designs are needed to decrease the thermal resistance between them and forced air streams. Manufacturing methods such as extrusion, machining and die-casting have been used to fabricate conventional longitudinal fin designs. Although these technologies add relatively little cost, they preclude the fabrication of more complex heat sink designs. We discuss novel heat sink designs which increase surface area and/or modulate air flow streams. Fabrication of these unconventional designs is enabled by using 3D printing technologies with the subsequent conversion of the printed parts into monolithic copper structures by investment casting.Mechanical Engineerin

THERMAL-RESISTANCE MEASUREMENTS ON MECHANICAL GAP FILLERS IPACK2005-73084

ABSTRACT This paper discusses spring-loaded mechanical structures that can be used to make thermal connections between an object to be cooled, such as an integrated circuit, and a dissipative structure, like a cooling plate or heat sink. These metal structures are flexible and resilient, adapting to variations in orientation of the two objects to be coupled. Precision experiments and computations demonstrate that they have much lower thermal resistance than elastomeric "gap-filler" pads that are usually used to perform this function. . INTRODUCTION A common problem in electronics packaging is to make a reliable, low-thermal-resistance connection between two objects whose separation is not reproducible. A typical example is an integrated circuit (IC) on a printed circuit board (PCB) in a circuit pack with a board-stiffener plate that is parallel to the PCB and which can draw heat away from the IC if sufficient thermal coupling can be achieved. Another example is an IC inside a closed EMI shield. Since an external airflow can only cool the outside surface of the shield, a thermal connection must be made between the IC and the enclosure. The problem in both cases is that variations in IC stack-up height and dimensional changes due to stress and warm-up can cause variations in the spacing between the heat source and the cooled structure. The usual solution to these problems is to design an open gap into this thermal path and to fill this gap with thermal grease or a gap-filler pad. These materials, however, have low thermal conductivities and poorly-controlled mechanical properties. In this paper, we describe mechanical structures that overcome many of these problems. Our designs consist of mating metal parts that slide, bend, or otherwise deform so as to provide the dimensional variation required to fill gaps in the thermal path between a heat source and a dissipative element. Thermal contact between the mating metal parts is made with thin layers of thermal grease whose thickness does not change as a function of applied pressure. Thus, the high thermal resistance associated with thick layers of low-conductivity materials is avoided. Resilience is provided by springs, whose elastic properties can be chosen to match the mechanical requirements of the system. We describe several of these structures, and we present precision measurements of the thermal resistance of two particular structures, as well as a comparison with a commercially-available gap-filler pad. Our basic result is that mechanical gap fillers function far better than alternative solutions to this ubiquitous problem. NOMENCLATURE FLEXIBLE STRUCTURES In this section, we describe some of the mechanical gap-filler structures we have designed. These structures were designed to bridge a gap of nominal height 12 mm with a range of height variations of nominally ± 1 mm. A base area of 40 mm x 40 mm was used in our designs, while the two structures which have actually been fabricated and tested have a base area of 35 mm x 40 mm. All thermal resistances quoted in this paper are normalized to a base area of 40 mm x 40 mm. Thermal contact between the mating fins is made using Thermagon T-grease 401, whose thermal conductivity is 0.6 W/m-K. As the structure is compressed, the overlap area of the fins increases, but the thickness of these grease layers does not change. Thus, our measurements show that the thermal resistance of this device, measured between its top and bottom faces, varies linearly with its height but does not otherwise suffer from degradation due to the presence in the thermal path of thick layers of low-conductivity materials. The resistance of the structure could be reduced by designing thinner gaps between the fins, thus producing thinner grease layers. This geometrical change would reduce the angular range over which the device can adapt to tilt. Another strategy for reducing the overall thermal resistance would be to use a larger number of thinner fins. We have not attempted to optimize this aspect of the device. The mechanical design of a structure like that in The structure must be designed with the appropriate uncompressed height; clearly, one would like to adjust the geometry so that the fins have as much vertical overlap as possible, even in the fully extended condition shown in The basic design constraint here is that the aggregate spring constant has to be sufficiently large that, under the conditions encountered in the application, the applied pressure is 5 to 10 psi. This is the pressure required to adequately compress the layers of thermal grease that are applied to the top and bottom surfaces of the structure, so as to minimize their thermal resistances. prototype of this structure having the same size as the singlenested structure in Copyright © 2005 by ASME were 1.0 mm thick x 3.0 mm tall; the upper and lower fin lengths were 35.0 mm and 22.6 mm, respectively (as in the single-nested-heat-sink design, the overlap region is not square, so there are two different fin lengths). The gaps between neighboring fins were again 0.2 mm, as in the previous design. Because the fins are shorter in this design than in the previous one, their area of overlap is smaller, and the total thermal resistance is higher for the same compressed height. The two nested-heat-sink devices described above are the only new structures that we have constructed and tested. Before describing our measurement system and the results, however, we present three other concepts for resilient, mechanical gapfilling structures. In the latter case, the two sets of open fins would overlap, but the gaps between them would be left wide enough for air to pass through them. Extending the bottom plate and adding fins to the extensions would provide a more direct thermal path from the heat source to the cooling airflow than the topplate fins that are shown, but an extended lower plate may be prohibited by the heights of neighboring components. Figure 4 shows a simpler method of thermally coupling the upper and lower surfaces: a base plate with a peg that can slide in and out of a mating hole in an upper plate. The surfaces of contact between the peg and the hole are coated with thermal grease. As before, springs provide resilience. This structure can adapt to changes in height, but its ability to adapt to nonparallelism between the upper and lower surfaces is limited, since the grease-filled gap should be thin. In the embodiment shown in upper block, allowing compressibility. In addition, the greasecovered convex lower surface of the rod mates with the concave depression in the upper surface of the lower block. This allows the structure to tilt over a wide range without changes in thermal conductance. (One could also make this structure out of only two blocks, with spherical mating surfaces. This simpler structure would exhibit large adaptability to tilt but no resilience.) heat-sink structures and of a structure consisting of a commercial gap-filler pad combined with an aluminum block to build up the same height as the uncompressed nested-heatsink structures. In addition to these basic experiments, we made measurements on bare and grease-coated aluminum blocks, as described below, that are not resilient but which provide baseline data for correcting the raw measurements on the flexible structures. We have also performed extensive numerical computations of the conduction of heat through these and related structures, using ICEPAK® CFD software (data not given here). The basic result of these numerical experiments is that all the novel flexible structures exhibit substantially lower thermal resistance than the present state of the art. Our experimental results bear out this conclusion. APPARATUS The measurements we wish to perform are conceptually straightforward: one heats one face of a structure under test and measures the resulting temperature difference ∆T across the structure, with thermal insulation to ensure that all the applied heat Q passes through the structure under test. The total thermal resistance is then simply R = ∆T/Q. In addition, since the structures we are examining are resilient, we need to apply a measured force F across them and measure the resulting structure height h. We are particularly interested in the behavior of the thermal resistance as a function of applied pressure P = F/A, where A is the area of the structure. This apparatus has a number of useful attributes. Chief among these is that it is very easy to insulate it thermally, since most of the heat is geometrically constrained to pass through the two structures under test. Simple blocks of polyurethane foam surrounding the center of the stack reduce stray heat losses to negligible values. The use of thermoelectric coolers (TECs) to control the temperatures of the outer plates allows us to apply mechanical force to parts of the apparatus (namely, heat sinks that are used to cool the TECs) that are not part of the thermal path that is being measured. Thus, the force measurements do not compromise the thermal measurements. Finally, we regard it as an advantage that the apparatus averages the properties of two copies of the structure under test in the same experimental run. The central heater block consists of two identical, 35-mmsquare, thin-film heaters glued between three copper blocks using silver-loaded conductive epoxy. Its outer dimensions are 40 mm square x 11.7 mm thick. The square faces of the assembled heater block were fly-cut parallel and polished with fine diamond polishing paper. The two heaters, whose resistances match to within better than 0.1%, are connected in series to a power supply via a 4-terminal system that measures the applied voltage and current. The applied power Q can thus be measured with a precision of better than 0.1%. This is our first primary measured quantity. The temperature T hot of the central copper plate is our second primary measured quantity. It is sensed by a 0.020"-diameter thermistor bead inserted into a grease-lined, 0.025"-diameter X 0.25"-deep hole in the center of the plate. The thermistor is excited and read by a DC bridge circuit with negligible selfheating. The thermistor is wired as one arm of the bridge; a second arm consists of a decade resistor box, allowing the bridge to be nulled with a step resolution equivalent to 0.002°C. Thus, our direct measurement is of the resistance at null, which can be estimated with a precision equivalent to better than 0.001°C. The null resistance is carefully calibrated against temperature in situ using a quartz-oscillator temperature probe (HP model 2804A), over a range of temperatures near room temperature. The quartz thermometer has been calibrated in turn against the ice point of deionized water with an accuracy of about 0.001°C. The specifications of this instrument state that sequential measurements made over short time periods have a relative precision of better than ±0.001°C. Including a calculation of the dependence of our DC bridge circuitry on room temperature variations, we estimate that the total uncertainty in the measured values of T hot is approximately ±0.002°C. As the total temperature excursions measured in these experiments ranged from 0.3°C to 1.1°C, our raw experimental precision in thermal-resistance measurements is better than ±1%. The two outer plates in the apparatus are made of fly-cut copper and have also been polished with fine diamond paper. Each plate is glued to and cooled by a TEC whose hot outer face is attached to a fan-cooled heat sink. The temperature of each plate is sensed by a thermistor bead and DC bridge circuit, as above. The TECs are driven by PID controllers (Linear Research model LR-130), which stabilize their temperatures to within about ±0.002°C. We have developed a transfer technique, using a third thermistor probe, to generate a list of pairs of null resistances for these two DC bridges that hold the two outer plates at equal temperatures, over a ±6°C range around room temperature. The quartz probe used for calibration of the thermistor in the heater block is also used during the experiments to monitor room temperature near the apparatus. These measurements have an absolute accuracy of better than 0.05°C. An important advantage of using high-precision thermometry in these measurements is that the temperatures encountered inside the central part of the apparatus never have to differ from room temperature by more than about 1.0°C. At this temperature difference, the Grashof numbers in the gaps and cracks in our foam insulation blocks are estimated to be less than about 10. Thus, convection is always weak or absent, and simple estimates put the conductive heat losses through the insulation and wiring at less than 1% of the total heat dissipated by the central heater block. Force is applied to one side of the measurement stack by an adjustable jack, via a load cell whose uncertainty that ranges from 0.01 to 0.07 kg, depending on the structures under test. This is negligible compared to the measurement range, which is over 20 kg. The opposing side of the stack is immobile. To measure the thickness of the resilient structures, we have glued a copper deflection-measurement tab to the heat sink of the moveable side of the stack. Its position is read by a micrometer with a resolution of about 0.003 mm. To account for the resilience of the nominally rigid parts of the apparatus, we made calibration measurements of the micrometer reading as a function of applied force, using bare, incompressible aluminum blocks as the test structures. Because of the slightly compliant mountings of the heat sinks, the apparatus exhibits a measured spring constant of 3350 ± 160 lb/in. This is far higher than the spring constants of the resilient gap-filler structures under test, which are of the order of 50 to 100 lb/in. We correct our deflection measurements on resilient structures to account for the resilience of the apparatus. The uncertainty in this correction dominates the RMS uncertainty of our thickness measurements, which is estimated to be ±0.016 mm. EXPERIMENTAL PROCEDURES The basic procedure in these experiments is to apply a desired force to the structure under test, set the two outer plates at equal temperatures T cold , and make measurements of the heater temperature T hot at several different heater powers Q, taking care to wait for thermal equilibration in between measurements. The dependence of (T hot -T cold ) on Q gives the raw measured thermal resistance. Two details complicate this simple procedure: how to minimize the effects of slow drifts in the room temperature, and how to properly extract the thermal resistance and its uncertainty from the data points. For each applied force F, we made temperature measurements at five to seven different heater powers Q, starting and ending at Q = 0 to track any drifts. The range of powers is chosen so that the total excursion of T hot for each value of F is less than about 1°C. For each new value of F, we reset the cold-plate temperature to track room temperature T room as it drifts during the day, so that T hot and T cold never differ from T room by more than 1 °C. Auxiliary measurements made far from T room show that its drifts have a negligible effect on the measured thermal resistances. This insensitivity is the principal advantage of high-precision thermistor thermometry. Typical data and results are shown in BACKGROUND MEASUREMENTS In all measurements on mechanical gap-filler structures, the top and bottom surfaces of the structures under test were covered with thin layers of thermal grease to minimize the thermal resistances of these interfaces. We performed a series of background measurements that allow us to estimate thes