Power density

National and urban power densities

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National and urban power densities As with the global rate, nationwide power densities of energy use become meaningful only when the annual supply of fuels and electricity is prorated over those areas where most of it converted to final uses (or at least taken onboard), that is when adjustments are made for energy use in a nation’s urban areas. Not surprisingly, US with its data abundance, makes the calculation relatively easy. American energy statistics are excellent, and we now have at least four studies of the nationwide extent of urban areas or the ISA. The US Geological Survey put the first nationwide estimate of urban areas at 90,000 km2 (USGS 2000). The first US study of the extent of the ISA used a 1-km grid for the coterminous states to combine information from nighttime lights radiance with land cover derived from LANDSAT coverage, and it put the total extent of the US ISA at nearly 113,000 ± 13,000 km2, slightly less than the surface of Ohio (Elvidge 2004).

Elvidge et al. (2007) lowered the total to about 84,000 km2, close to the USGS study. Churkina, Brown and Keoleian (2010) came up with a higher total of 141,000 ± 40,000 km2 for the year 2000, and they also calculated that grassy surfaces cover about 40% and treed surfaces extend over about 25% of America’s urban areas. Correcting for these vegetated surfaces would bring the mean total of the true ISA to about 50,000 km2. Correcting for final energy uses that take place outside urban areas can be done with fairly small errors. I assume first that 80% of electricity is generated outside urban areas, and then I assume that 85% of all residential, 90% of all commercial, 75% of all industrial and 50% of all transportation energy use takes place in urban areas; their annual energy demand would have amounted to about 55% of the countrywide total of 3.25 TW in 2011, or nearly 1.8 TW. With the extremes of 84,000 and 180,000 km2 in the denominator this would translate to 10-21 W/m2.

Excluding all vegetated surface and putting 50,000 km2 in the denominator would raise the average US urban power density of energy conversions to about 35 W/m2. The rates of 10-35 W/m2 based on generalizing approximations are well supported by rates calculated by bottom-up sectoral aggregations for specific US cities as well as for urban areas in an increasing number of other (mainly European and Asian) countries. Recent work on these anthropogenic heat releases (or emissions) spans scales from global assessments to appraisals at national and city level and to microstudies of specific wards in large cities (Hsie, Aramaki and Hanaki 2007; Allen, Lindberg and Grimmond 2011; Chen et al. 2012; Wong, Dai and Paul 2012).

There are also many kindred studies of urban heat islands –- perhaps most notably, Peng et al. (2011) used surface temperature difference between urban and suburban measured from the MODIS satellite to quantify them for 419 of the world’s big cities -– but their results (expressed as temperature differences in additional 0C) cannot be readily translated into power density of specific urban energy use. And I should note that there is also a downward anthropogenic heat flux creating a subsurface urban heat island but, naturally, its intensity is a tiny fraction of the surface counterpart. Menberg et al. (2013) actually calculated that in Karlsruhe the average total heat flux into the city’s shallow aquifer was about 760±89 mW/m2 in 1977 and that by 2011 it increased to nearly 830±143 mW/m2.

Power densities of urban anthropogenic energy dissipation have several key attributes in common. They display expected daily, weekly and seasonal fluctuations (daily maxima between 11-18 of the local time; weekend lows; winter maxima in cold regions); their most common annual means range between 10-100 W/m2 but seasonal extremes for the smaller areas with the highest energy use can go up to, and even above, 1,000 W/m2, exceeding energy received in some locations even during the peak noon time; in the past cities in cold climates had the highest pronounced winter peaks but very high rates are now prevailing even in tropical climates due to the emergence of high-rise-filled downtowns and ubiquitous air conditioning; and, naturally, they peak in central business districts of megacities and decline toward the fringes of conurbations.

Bottom-up approaches used to quantify these urban power densities have relied on a wide range of relevant statistics (including population densities, human metabolism, energy use by buildings and industries; density of road transport and typical specific energy demand of cars, buses and trucks) incorporated in often detailed models. Quah and Roth (2012) present more than two scores of annual (and also seasonal) power densities published between 1952 and 2009 for cities in US, Canada, Europe and Asia: annual extremes in this set are just 4-5 W/m2 for suburban areas of smaller cities (Swiss Basel and Polish Łódź) and 159 for Manhattan in 1967, the modal range was between 11-30 W/m2, and Tōkyō in 1989 had the hourly extremes (for both summer and winter) at, respectively, 908 W/m2 and 1,590 W/m2 (Ichinose, Shimodozono and Hanaki 1999). Among notable recent bottom-up calculations are those of Hsie, Aramaki and Hanaki (2007) for Taipei, Iamarino, Beevers and Grimmond (2012) for London, Quah and Roth (2012) for Singapore and Howard et al. (2012) for New York City, and Hong Kong’s excellent statistics make it possible to calculate specific power densities for one of the world’s most densely populated urban areas.

High-resolution (both in space and time) assessment for London shows that human metabolism contributes just 5% of the mean annual anthropogenic flux of 10.8 W/m2 for 2005-1008, that domestic and industrial sources are nearly equal (4.6 and 4.1 W/m2) and that road fuels contribute about 15% of the total (1.65 W/m2). As expected, the rates decline towards the outskirts of Greater London and less than 3% of the city had values above 50 W/m2, with the City of London (highest density of high-rise buildings, 348,000 daily workers within 3.2 km2 in 1007) going up to 140 W/m2 with local peaks up to 210 W/m2. Sensible heat dominates the flux, latent heat carries away only about 7% of thermal energy and heat transferred first to wastewater accounts for about 12% (Iamarino, Beevers and Grimmond 2012).

In Singapore 24-hour maxima reach 113 W/m2 in the commercial district, 17 W/m2 in high-density public housing and 13 W/m2 in the low-density residential areas, with buildings (primarily due to cooling) being the largest source of dissipated heat, 49-82% on weekdays and 46-81% on weekends (Quah and Roth 2012). In DaAn ward of Taipei city daily heat rejection by air-conditioned buildings averaged 15 W/m2 for residential housing and 75 W/m2 for commercial establishments, with the overall mean of 34 W/m2 (Hsieh, Aramaki and Hanaki 2007). The most informative of these studies of urban energy use is a city-wide mapping on a block- and lot-level for New York (Howard et al. 2012).

Its authors estimated annual building energy use through multiple linear regressions of ZIP code-level energy demand for electricity, natural gas, fuel oil and steam for the year 2009 and building information from the New York City Department of City Planning geographic database, and they expressed energy use intensity (a synonym for power density) in delivered rather than primary energy terms. By far the most interesting part of their presentation is their map of power densities using block land area in the denominator. Some mid-Manhattan blocks with high density of high-rises show power densities as high as 900 W/m2 which means that a single block demands year-round average of nearly 18 MW of delivered energy. Other parts of the city where many blocks have power densities in excess of 400 or 500 W/m2 are in the financial district, Greenwich Village, Flatiron, Midtown South, Sutton Place and East Side. Manhattan’s lowest power densities are in Harlem and East and West Village, and densities in residential boroughs are generally below 25 W/m2 and city blocks in parts of Queens and Staten Island rate less than 15 W/m2.

Hong Kong’s energy statistics list end uses for residential, commercial, industrial and transportation sectors (Hong Kong Electrical & Mechanical Services Department 2013) and detailed land use data (Hong Kong Planning Department 2013) make it easy to reconstruct specific power densities on annual basis. In 2012 average power density of residential energy use was about 40 W/m2, a relatively high rate reflecting the dominance of the city’s crowded high-rise housing estates; power density of industrial areas was about 20 W/m2 and that of land transportation reached a very high rate of about 50 W/m2 while the overall rate for the city’s impervious surfaces (Hong Kong has only a minuscule agricultural sector) was roughly 60 W/m2.

Power densities of buildings Not surprisingly, the order of magnitude will not change as we narrow the spatial focus from the most densely built-up city wards to individual buildings, or from areas of the heaviest traffic to individual roads or crossroads. Nationwide means of power densities of America’s building stock can be readily calculated from statistics in Buildings Energy Data Book, a detailed compendium maintained by the USDOE (2013). Its disaggregated annual totals show the 2010 site use average (that is with fuel-based electricity not converted to its primary energy equivalent) of 40 W/m2 for commercial buildings (with space heating claiming 27%, cooling 10% and water heating less than 7%), and just over 16 W/m2 for residential buildings, with about 45% of that rate due to space heating, more than 16% used by water heating and about 9% by cooling.

US residential lighting needs less than 6% of all electricity, with power density just below 1 W/m2. Commercial indoor lighting claims almost 14% of the total usage (about 5.5 W/m2). Disaggregations by building function for New York City by Howard et al. (2012) showed energy use per floor area ranging from just over 20 W/m2 for residential housing (for 1-4 families) to about 35 W/m2 for multifamily residential housing and almost 70 W/m2 for stores, schools and hospitals. One of America’s best sources for power densities of energy use in a large number of specific buildings (rather than averages drawn from nationwide aggregates) is San Francisco’s annual Energy Benchmarking Report that lists electricity and fuel uses of hundreds of municipal structures (San Francisco Water Power Sewer 2013).

Modal ranges in the ascending order of densities for 2012 are (all values in W/m2 of floor area and for energy used on-site): parking garages 2-6, warehouses 5-11, schools 15-22, offices, libraries, performance halls, conventions centers, police and fire stations 22-35, museums 35-100. As expected, modern offices, schools and retail space have roughly similar specific energy requirements, on the order of 20-30 W/m2 of floor area, less than half than do supermarkets (they were even more wasteful in the past due to open-bin freezers) and as little as a third of the rate for busy restaurants and hospitals.

As I have clearly indicated, all of these densities refer to energy required per unit of floor space and hence equal the power densities used in this book (energy consumed annually per a structure’s footprint) only for single-story buildings and have to be appropriately multiplied for multi-story structures. And it should be also noted that expressing the rates in terms of primary energy would roughly double the usually quoted end-use values: actual multiples were 2.1 for commercial and 1.9 for residential buildings, raising the densities to, respectively, to 84 W/m2 and 30 W/m2. This is, of course an inevitable consequence of two unalterable realities: all modern buildings require large inputs of energy for lighting, air conditioning, appliances and electronic devices (some also for heating and water heating), and in most countries (including the US) most of the delivered electricity comes from thermal generation with its inherently large conversion losses (best efficiencies now around 40%).

Consequently, when expressing power densities of buildings care must be taken to specify if they refer to per unit of floor area (as is commonly done in publications on energy use in buildings) or per a structure’s footprint (as I do here in order to make all power densities comparable). And when comparing international power densities of energy use in buildings or when reviewing long-term trends in energy use it is also imperative to use the same accounting units, that is either end-use (on-site) energy or primary energy. Comparing the energy performance of buildings simply by referring to their power densities is misleading: corrections must be made for the average number of heating and cooling days, for the primary sources of used energy and for the ownership of electricity-consuming appliances and electronic devices; moreover, preferred indoor temperatures and appropriate levels of lighting should be also taken into account.

For example, my superinsulated house (2” x 6” frame with fiberglass in walls, thick layer of blown insulation in the attic, exterior styrofoam wrap around the foundations, triple windows with argon, 97% efficient natural gas furnace) will use more energy (averaging 35 W/m2) than an indifferently built house in Vancouver. The two cities have the same latitude (500N) but during 2013 the Winnipeg’s mid-continental location brought 2.6 times more heating-degree days than Vancouver’s much warmer maritime climate (Degree Days.net 2013). Such differences will always remain, but historical evidence is clear: better construction, more efficient heating and cooling, less electricity-intensive appliances and less wasteful lighting have translated into fairly impressive declines of average residential power density in every climate.

As a result in many fairly large differences in power densities of individual buildings are more due to design and operating practices rather than to disparities in climates and preferred indoor temperatures. European data show that power densities of single-family house heating in Germany had hardly changed between 1918 and 1957 (nearly 30 W/m2) but then declined to 18 W/m2 by 1967 and to just 6 W/m2 in 2010; in the UK the drop was from about 66 W/m2 before 1920 to 23 W/m2 by 2002, and in Italy from 25 to about 10 W/m2 between 1950 and 2005 (BPIE 2011).

Between 1980 and 2005 the average US rate declined by 37% for all housing units, by 45% for single-family detached houses in the South (EIA 2009). How far these declines can go? There are now many new low-energy office buildings –- designed to maximize the benefits of natural energy flows, often relying on heat pumps and equipped with the most efficient lighting, heating and cooling system -– whose power densities are an order of magnitude lower than those of average structures (the US primary energy means being roughly 30 W/m2 for houses and 80 W/m2 for commercial buildings).

For example, Canada’s most efficient office building, headquarters of Enermodal Engineering in Kitchener, Ontario, draws only 8.5 W/m2 of floor area, only a tenth of the country’s typical multistory office structure (Enermodal Engineering 2013). The most energy-efficient building in the US, Seattle’s Bullitt Center (with large PV array, geothermal heating and cooling and motorized windows), is in a much warmer climate and its demand comes at just 6 W/m2 of floor area (Bullitt Center 2013). Best house designs can result in similarly low rates but zero-energy house in any colder climate is a misnomer: the house may not need any external source of energy but (even with efficient passive design) it will require a substantial investment in a PV or a geothermal system or both.

Finally, it is revealing to add up the energy uses per unit of floor area to get (annualized) ascending range of power densities of common, as well exceptional, buildings. Well-built, that is highly energy-efficient, single-story house in mild maritime climate that requires minimum heating and no cooling could average less than 10 W/m2. The two super-efficient office buildings are both low-rises: Enermodal is only three stories high and Bullitt venter has just six stories and hence their average power densities are, respectively, just 25.5 and 48 W/m2. Modern (post-1990) American detached two-story house will average between 30-40 W/m2 of its foundation, and an older (pre-1980) 20-story office buildings in climate that requires both heating and cooling will average 800 W/m2. Buildings in Kwai Chung, Hong Kong’s largest public housing estate in New Territories with 16 towers of 38 floors and almost 25 W/m2 of floor area, will have power density of roughly 950 W/m2; that is (as already shown) the same as the most energy-intensive city blocks in Manhattan’s Midtown.

Mid-price and luxury hotels have always had above-average energy needs per unit of floor area: average for the US hotels has been 45 W/m2, in much colder Ottawa it is 77 W/m2, in London (due to poorly insulated buildings and inefficient heating) as much as 80 W/m2, in Hong Kong (due to air conditioning) 63 W/m2, but average in Auckland’s moderate climate it is only about 30 W/m2 (Deng and Burnett 2000; Su 2012). This means that even now common 10-story buildings will have power densities of up to 800 W/m2 and that the tendency to raise many modern luxury hotels to more than 50 stories creates exceptionally high power densities, particularly in desert climates. A 50-story hotel in hot climate will have power density of close to, or in excess of, 2,000 W/m2 and Burj Khalīfa, the world’s tallest building (828 m, 160 floors) in Dubai, has the base footprint of 8,000 m2 and peak electricity demand of 50 MW, implying temporary power densities up to 6,250 W/m2 of its foundation.

Transportation densities Energy dissipated by road traffic is an important component of urban energy use. Although usually a much smaller aggregate contributor than domestic demand and industrial processes -– for example, disaggregated data for Greater London between 2005 and 2008 show the three shares at, respectively, 42%, 38% and 15%, with metabolism accounting for the rest– urban traffic can reach very high power densities along major heavily-travelled roads even when it flows freely, and even higher rates in prolonged traffic jams when all but a few drivers keep their engines idling. This is an inevitable consequence of relatively low efficiency of gasoline engines as they lose about 30% of purchased fuel through their radiators and about 40% in their exhaust gases.

Most of the latter flux is redistributed by radiation before it exits a tailpipe: exhaust temperature is less than 700C while the gases leaving the cylinder have temperature of about 8000C. Both radiator heat and exhaust heat are absorbed first by other car structures before they are finally lost to the atmosphere where they add to heat generated by driving. The logical way is thus to use a car’s footprint rather than just footprints of a radiator or exhaust system as the denominator in calculating vehicle power densities. Small cars have footprint of less than 4 m2 (3.8 m2 for Honda Fit), large ones go over 5 m2 (5.1 m2 for Mercedes-Benz S class). With power ratings of, respectively, about 87 kW and 339 kW, the maximum theoretical power densities of energy use by those two vehicles would be 22,900 Wt/m2 and 66,500 Wt/m2 of their footprint, the rates resembling power densities of heat dissipation in large power plant cooling towers.

Heat dissipated from vehicles is, of course, diffused along roads, driveways and parking lots. Maximum short-term rates of automotive heat dissipation depend on roadbed widths (3.6 m is the US standard for freeways, 2.7-3.6 m on local rods), speeds, distances between vehicles and their power rating. Freely-flowing car traffic on a freeway (30 cars/km per lane at 80 km/hour) with cars averaging 8 L/100 km (29 mpg) will have power density of about 475 W/m2 of paved lane. A mixture of 70% cars and 30% trucks with 1,000 vehicles/km of a single lane in one hour would generate power density of about 560 W/m2:

Power density of highway traffic

1,000 vehicles/hour/lane (width 3.6 m)

700 cars and 300 trucks

cars 4 kJ/m 700 x 4 kJ x 1,000 m = 2.8 GJ

trucks 15 kJ/m 300 x 15 kJ x 1,000 m = 4.5 GJ

7.3 GJ/3,600 = 2.03 MW/3,600 m2 = 563 W/m2

In a traffic jam, with 125 idling vehicles per km of street lane just 3 m wide and consuming about 1.3 MJ/minute (roughly 21 kW per vehicle) the stationary power density will reach 900 W/m2.

These high rates apply only to the lanes with high-density traffic or to temporary stoppages. Appropriate inclusion of associated road infrastructure would commonly halve those rates and often reduce them even more. Paved shoulders on US Interstate highways have minimum width of 3.05 m on the outside and 1.22 m on the inside, medians have minimum width of 11 m in rural and 3 m in urban areas. Inclusion of these surfaces for a four-lane highway would reduce all of the just calculated rates by at least 57% and usually more than 60% in rural settings, resulting in rates below 250 W/m2 in flowing traffic. Inclusion of adjacent land that forms the entire road infrastructure (ditches, embankments, graded slopes, land cut-off by approaches, exits and cloverleaf interchanges) would commonly bring further reductions on the order of 20%-40%, that is to rates well below 200 W/m2 of entire transportation corridor in flowing high-density traffic.

Adjustments of these calculated short-term peak rates for average annual traffic, with its enormous fluctuations between near-empty roads of early morning hours and seemingly endless congestions of rush-hours, cuts the rates by an order of magnitude. The next adjustment to calculate long-term power densities of urban traffic is to prorated it over the entire area devoted to roads and parking lots, with the former claiming about 30% of all land (35% in many US cities) and the latter at least 20% of the total. This means that prorating the road transport energy use over the entire city area will cut the density by about two-thirds, to rates below 5 W/m2, compared to the rates derived by having only road infrastructure in the denominator.

Actually calculated means of urban traffic power densities in Greater London during the years 2005-2008 were 1.65 W/m2 (Iamarino, Beevers and Grimmond 2011). Recent gasoline consumption data for Los Angeles county, the epitome of high-density traffic, show annual purchases running at the rate of about 72 GW. Even when assuming that only a third of all gasoline purchased in the county is actually consumed within its borders this would prorate to 2 W/m2 for the county’s entire area, or 4 W/m2 for its residential and industrial land, and addition of diesel fuel (assuming the nationwide proportion of gasoline/diesel use is valid for LA) would raise this to at least 5.5 W/m2.

Challenges of heat rejection

Many energy conversions do not require any special arrangements to dissipate the resulting heat, just cautious handling of hot light bulbs, toasters and irons, and avoidance of hot cooking surfaces. In many other instances the task can be done with relatively simple arrangements: fins on radiators (be they in engines, industrial settings or in room heating using circulating hot water) increase the overall surface area and accelerate heat transfer. In contrast, even the most efficient large thermal electricity-generating stations have to reject about 60% of the initial energy input as waste heat and such large energy fluxes require special accommodations. Losses through hot working surfaces are minor, with cooling water carrying away the largest share of converted fuel.

As already described, cooling towers are built to reject about 50% of all energy used by thermal power plants to generate electricity, and large natural draft units (the largest ones are massive concrete structure up to 100 m in diameter and up to 200 m tall) are designed for fluxes of 20-40 kWei/m2. But with typical fuel conversion efficiencies of about 40% a power plant with installed capacity of 2 GW will reject about 2.5 GWt through its cooling towers and actual heat rejection power densities will be close to 80,000 Wt/m2 of their footprint. Actual rates for the entire space claim will be lower because these large towers must be set well apart in order to prevent Venturi effect-induced wind loads on their relatively slender concrete walls. Cross-flow cooling towers using mechanical draft units are even more compact with throughput power densities of 100,000-125,000 Wt/m2.

Not all of the heat carried by combustion gases is transferred to boiler tubes to raise steam; some of it is recovered to preheat combustion air and water fed into the boiler but about 10% of plant’s initial fuel input is rejected through a stack. With 40% conversion efficiency this amounts to about 500 MWt for a 2 GWe station. Tall chimneys (scores of the tallest ones have surpassed 300 m) have top inside diameter of just 3-7 m and bottom inside diameter of 14-17 m, which means that they reject heat with power densities of 0.7-1 MWt/m2 of their foundations. Introduction of FGD changed because flue gases (120-1500 C) must be cooled to saturation temperature before their SO2 reacts with alkaline compounds and they leave stacks at less than 500C producing heat rejection power densities an order of magnitude lower than do the traditional arrangements.

But the greatest technical heat rejection challenge does not take place on the just described macroscale of large thermal electricity-generating plants or on much moderate scale of various internal combustion engines (Otto and Diesel cycle, gas turbines) but on microscale thanks to ever increasing crowding of transistors on tiny surfaces of microprocessors. History of this challenge has been documented in great detail. Intel 4004, the world’s first microprocessor (commonly known as microchip) was released in 1971 and its 2,300 transistors placed on 135 mm2 silicon die dissipated about 2.5 W/cm2 (Intel 2013). In 1978 Intel 8086 contained 29,000 transistors and it dissipated 7.6 W/cm2 almost exactly as much as a small (160 cm2) circular kitchen hotplate rated at 1,200 W.

By the beginning of the 21st century Intel’s ultra large scale integration procedures crowded 50 million transistors on 130 mm2 of Xeon Irwindale whose demand of 115-130 W prorated to up to 100 W/cm2, equivalent of 1 MW/m2 and in 2005 Pentium 4 went above 100 W/cm2 (Azar 2000; Joshi 2001; Intel 2005). Moreover, heat fluxes in a microchip’s hot spots can go briefly as high 1,000 W/cm2; this power density is equal to about 15% of the flux through the Sun’s photosphere (64 MW/m2) or through a rocket nozzle (7,000 W/cm2). Standard operating densities on the order of 100 W/cm2 are, as noted earlier in this segment, of the same order of magnitude as heat rejection created by hot flue gases ascending through a large stack and it far surpasses the rate of convective heating that used to be generated by the US Space Shuttle’s re-entry into the atmosphere and that exposed thermal protection system tiles to about 6 W/cm2 and leading edge (reinforced carbon-carbon) to about 60 W/cm2 (Harvey 2008).

Subsequent microprocessor redesigns reduced the heat flux: in 2006 Core 2 Duo (thermal design power of 65 W) was below 50 W/cm2 and by 2010 Intel’s Atom was back to hot-plate power density of 10 W/m2 (Pant 2011). Naturally, microprocessor heating and heat rejection take place over a much smaller areas than in space vehicle tiles exposed to re-entry speeds or in coal-fired plant stacks, but that does not make the heat dissipation challenge any easier. Microchips are usually placed in a very tight confinement but in order to insure their optimum performance their temperature should be kept below 450C or else their operation will slow down and eventually cease. As a result, designers of printed circuit boards are forced to come up with many ingenious arrangements to manage high heat fluxes (Allan 2011).

This challenge becomes even greater when servers and disk storage systems are stacked in data centers in racks. A standard server rack, placed on raised floor with perforated tiles or grates, has been 2.1 m tall, composed of 42 units of 48.26 cm (19 inches) wide slots, but some companies have preferred much taller racks (57 units by Microsoft) or wider (up to 58.42 cm) enclosures (Miller 2012). Footprint of a standard 42-unit rack is 0.478 m2 for the inside dimensions and 0.65 m2 for the cabinet. The rate of increase in product heat density has slowed down since the mid-2000s but even so servers and disk storage systems saw an order of magnitude rise in less than two decades, from just over 2,000 W/m2 in the early 1990s to 20,000 W/m2 by 2010 (Data Clean 2012). Most of the products deployed in large data centers have rated demand between 8-20 kW/rack and designers are working on servers of 30 kW+.

Other space definitions reduce this density: adding front and back clearances around server cabinets cuts the density by roughly two-thirds, adding shared aisles at the end of the row entails a further 25% cut, and including all main aisles and power delivery and cooling units brings the rate down to less than 20% of the rack density value (Brill 2006). Approximate conversion of product (rack) power density to gross computer room density is just 0.018. Moreover, some racks may be empty (held in reserve) while others may be only partially filled, and the centers rarely operate near their full capacity. On the other hand, for every 1 W used by servers up to 0.9 W have been typically needed for the electrical infrastructure that enables the servers, that is for uninterruptible power supply, switches, lighting and, above all (nearly 40% of all power), for cooling (Emerson Network Power 2008).

Representative data on power densities for data centers housing the servers –- based on information from 59 facilities in North America and Europe with areas ranging from less than 2,000 m2 to 18,000 m2 -- show these realities (Renaud and Mescall 2011). The studied centers were designed for median design power density of 730 W/m2, with some smaller centers rated for as much as 1,615 W/m2, but actually used power (gross computer room density) averaged only 437 W/m2 which means that the centers are using less than 60% of their available power; their median value per rack was only 2,100 W/m2, with the middle 50% ranging from 1,700-2,200 W/m2, and average power density per rack declines with the data center size. But some smaller centers may have overall densities (including all support system supply) on the order of 2,500 W/m2 (Emerson Network Power 2008).

Coping with less than 500 W/m2 in terms of gross computer room density is not an extraordinary challenge, but removing heat from racks operating with densities of 103 W/m2 and for entire rooms whose power density is in excess of 2,000 W/m2 calls for efficient cooling in order to maintain temperature between 10-350C and relative humidity below 80% (Minas and Ellison 2009; Pflueger 2010). This challenge is perhaps best illustrated by expressing the rack power densities in terms of power/volume. A high-rise apartment building in Hong Kong may have power density twice as high as a server room power density when both rates are expressed per unit of their footprint area (950 vs. 475 W/m2) but a server rack using 2,100 W/m2 will be rejecting about 1,000 W/m3 of its volume compared to less than 10 W/m3 of a 38-storey apartment building.

Uneven cooling, and hence recurrent hot spots, has been a common problem in data centers, with about 10% of racks getting too hot to meet the standards for maximum reliability: every increase of 100C above 200C cuts the long-term reliability of hardware by half (Uptime Technologies 2010). Cooling requirements of data centers have been rising but 70% of cooling capacity available in a typical computer room is wasted due to bypass airflow (Uptime Institute 2010). Reducing this waste by optimizing center layouts and maximizing efficient airflow are the best ways to limit the need for cooling capacity.

Global electricity demand by data centers had doubled between 2000 and 2005 (Koomey 2008) but between 2005 and 2010 (largely due to worldwide recession) it increased only by about 56%, and in the US it grew by just 36% instead of doubling again (Koomey 2011). In aggregate terms data centers used 1.1-1.5% of the world’s electricity (23-31 GW) in 2010 and the US share was between 1.7-2% (7.7-9.8 GW). But between 2011 and 2012 global power requirements rose by 63%, according to Datacenter Dynamics census from 24 GW to 38 GW, with 43 GW forecast for 2013 (Computer Weekly 2013). Given a rapid data growth -– Intel sees new information load rising from 2 zettabytes (1021 bytes) in 2011 to 8 petabytes in 2015 (Otellini 2012) -- further large increases of demand must be expected.

I will close this segment with a few observations on thermal consequences of energy use in general and concentrated heat rejection in particular. Proceeding from the smallest to the largest scale, it is obvious that the highest power densities of heat rejection are limited to such tiny areas –- as small as 10-4 m2 for microprocessors –- that the power fluxes of individual components are too small to have any discernible impact even on just a room scale. Keeping a microchip cool may be a challenge and careful design must be deployed to cool microprocessor in servers that are layered in tall racks -– but it is only in such rooms crammed with data processing assemblies where their operation dominates the overall heat balance.

In usual circumstances heat rejected by electronic devices represents a negligible addition to a room’s overall thermal background. For example, when I am using a laptop in my living room its operation will add some 60 W of dissipated heat compared to 400 W coming from recessed ceiling lights, 200 W from a stereo system, 85 W from my metabolism (assuming 20% mark-up above the basal metabolic rate while sitting) –- and (during a summer day) more than 1,500 W of sunlight that is coming in at noon through SW-facing windows, or (during cold winter evenings) about 1,000 W of hot air that is forced through floor heat vents when my natural gas furnace is heating the house.

Those anthropogenic heat rejection rates that are three orders of magnitudes above the peak insolation rates (that is 106 W/m2) are restricted to areas smaller than 102 m2 (bottoms of large power plant boilers, mouths of tall power plants stacks), and those flues that are one to two orders of magnitude higher than noon-time irradiance (that is between104-105 W/m2) originate from areas smaller than 100 x 100 m (mainly large cooling towers). Heat rejection by both tall power plant stacks and cooling towers is associated with substantial condensation and creation of often relatively large ascending clouds well visible on satellite images as well as with some recurrent local fogging and icing, but only rarely with any downwind precipitation anomalies.

Similarly, other concentrated heat rejection processes (ranging from hotplates and car exhausts to tall power plant stacks) are limited to relatively small areas: as power density of anthropogenic energy conversions increases the spatial extent of the more intensive heat rejection fluxes declines at a considerably faster rate. As a result, heat-rejection phenomena that constitute a significant share of solar inputs (101 W/m2) are limited to areas no larger than 108 m2, to large cities, extensive industrial regions and busy transportation corridors. As already noted, energy use in buildings, industries and in transport helps to turn large cities into unmistakable urban heat islands. Of course, other factors contribute to create this phenomenon: urban impervious surfaces have higher thermal capacity than grassy or treed areas and their heating will generate much stronger convective flows; albedo of many buildings and most parking lots and roads is lower than that of many natural surfaces; and restricted sky view in canyon-like streets reduces radiative cooling and sensible heat loss is larger than latent heat flux (Tasha 2004; Stewart 2011).

As a result, urban heat islands average commonly 20C more than the surrounding countryside and their most concentrated areas may be temporarily (especially during the night) as much as 80C warmer. While urban heat islands can explain only a negligible fraction of global temperature rise during the 20th century (Peterson and Owen 2005), they have a number of well documented impacts. Those include statistically significant (local and downwind) increases in cloudiness, precipitation and thunderstorms and reductions of relative humidity, wind speed and horizontal insolation due to shading. They also promote the formation of photochemical smog and accentuate summer heat waves with their premature mortality (Wong, Pardon and Jimenez 2013) and, in a positive feedback, increase energy use for air conditioning.

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