Academic literature on the topic 'Conditional moment closure'

This work presents a novel algorithm for supersonic combustion modelling. The method involved coupling the Conditional Moment Closure (CMC) model to a fully compressible, shock capturing, high-order flow solver, with the intent of modelling a reacting hydrogen-air, supersonic jet. Firstly, a frozen chemistry case was analysed to validate the implementation of the algorithm and the ability for CMC to operate at its frozen limit. Accurate capturing of mixing is crucial as the mixing and combustion time scales for supersonic flows are on the order of milliseconds. The results of this simulation were promising even with an unexplainable excess velocity decay of the jet core. Hydrogen mass fractions however, showed fair agreement to the experiment. The method was then applied to the supersonic reacting case of ONERA. The results showed the method was able to successfully capture chemical non-equilibrium effects, as the lift-off height and autoignition time were reasonably captured. Distributions of reactive scalars were difficult to asses as experimental data was deemed to be very inaccurate. As a consequence, published numerical results for the same test case were utilised to aid in analysing the results of the presented simulations. Due to the primary focus of the study being to assess non-equilibrium effects, the clustering of the computational grid lent itself to smeared and lower magnitude wall pressure distributions. Nevertheless, the wall pressure distributions showed good qualitative agreement to experiment. The primary conclusions from the study were that the CMC method is feasible to model supersonic combustion. However, a more detailed analysis of sub-models and closure assumptions must be conducted to assess the feasibility on a more fundamental level. Also, from the results of both the frozen chemistry and the reacting case, the effects of assuming constant species Lewis number was visible.

Lean premixed combustion is at present one of the most promising methods to reduce emissions and to maintain high efficiency in combustion systems. As the emission legislation becomes more stringent, modelling of turbulent premixed combustion has become an important tool for designing efficient and environmentally friendlier combustion systems. However, in order to predict these emissions reliable predictive models are required. One of the methods used for predicting pollutants is the conditional moment closure (CMC), which is suitable to predict pollutants with slow time scales. Despite the fact that CMC has been successfully applied to various non-premixed combustion systems, its application to premixed flames is not fully tested and validated. The main difficulty is associated with the modelling of the conditional scalar dissipation rate (CSDR) of the conditioning scalar, the progress variable. In premixed CMC, this term is an important quantity and represents the rate of mixing at small scales of relevance for combustion. The numerical accuracy of the CMC method depends on the accuracy of the CSDR model. In this study, two different models for CSDR, an algebraic model and an inverse problem model, are validated using two different DNS data sets. The algebraic model along with standard k-ε turbulence modelling is used in the computations of stoichiometric and very lean pilot stabilized Bunsen flames using the RANS-CMC method. A first order closure is used for the conditional mean reaction rate. The computed nonreacting and reacting scalars are in reasonable agreement with the experiments and are consistent with earlier computations using flamlets and transported PDF methods for the stoichiometric flames, and transported PDF methods for the very lean flames. Sensitivity to chemical kinetics mechanism is also assessed.

The accurate description of the turbulence chemistry interactions that can determine chemical conversion rates and flame stability in turbulent combustion modelling is a challenging research area. This thesis presents the development and implementation of a model for the treatment of fluctuations around the conditional mean (i.e., the auto-ignition and extinction phenomenon) of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software. The wider objective is to apply the model to advanced combustion modelling and extend the present analysis to larger hydrocarbon fuels and particularly focus on the ability of the model to capture the effects of particulate formation such as soot. A comprehensive approach for modelling of turbulent combustion is developed in this work. A direct quadrature conditional moment closure (DQCMC) method for the treatment of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software is described. The method which is based on the direct quadrature method of moments (DQMOM) coupled with the Conditional Moment Closure (CMC) equations is in simplified form and easily implementable in existing CMC formulation for CFD code. The observed fluctuations of scalar dissipation around the conditional mean values are captured by the treatment of a set of mixing environments, each with its pre-defined weight. In the DQCMC method the resulting equations are similar to that of the first-order CMC, and the “diffusion in the mixture fraction space” term is strictly positive and no correction factors are used. Results have been presented for two mixing environments, where the resulting matrices of the DQCMC can be inverted analytically. Initially the DQCMC is tested for a simple hydrogen flame using a multi species chemical scheme containing nine species. The effects of the fluctuations around the conditional means are captured qualitatively and the predicted results are in very good agreement with observed trends from direct numerical simulations (DNS). To extend the analysis further and validate the model for larger hydrocarbon fuel, the simulations have been performed for n-heptane flame using detailed multi species chemical scheme containing 67 species. The hydrocarbon fuel showed improved results in comparison to the simple hydrogen flame. It suggests that higher hydrocarbons are more sensitive to local scalar dissipation rate and the fluctuations around the conditional means than the hydrogen. Finally, the DQCMC is coupled with a semi-empirical soot model to study the effects of particulate formation such as soot. The modelling results show to predict qualitatively the trends from DNS and are in very good agreement with available experimental data from a shock tube concerning ignition delays time. Furthermore, the findings suggest that the DQCMC approach is a promising framework for soot modelling.

Time in the Blues presents an interdisciplinary analysis of the specific forms of temporality produced by and reflected in the blues. Often described as immediate, spontaneous, and intense, the blues focus on the present moment, creating an experience of time for both performer and listener that is inflected by the material conditions that gave rise to the genre. Examining time as it is represented, enacted, and experienced through the blues engages questions concerning how material conditions in the early twentieth century shaped a musical genre. The formal characteristics of the blues—ostinato patterns, cyclical changes, improvisation, call and response—emerge from and speak to economic, social, and political relations under Jim Crow segregation. A close examination of the structuring of time under sharecropping, convict lease, and migration reveals their significance to aesthetic constraints in the blues. Likewise, contexts and frames of reception, such as traveling shows, advertisements for 78 rpm records, and a sense of tradition structure the experience of time for an audience of listeners. Blues music provides a rich and complex articulation of a dynamic form of resonant temporality that speaks against the dominant culture through its insistence on the present moment. Ultimately, Time in the Blues, argues for the relevance, significance, and importance of time in the blues for shared values of community and a vision of social justice.

Relational Inequalities focuses on the organizational production of categorical inequalities, in the context of the intersectional complexity and institutional fluidity that characterize social life. Three generic inequality-generating mechanisms—exploitation, social closure, and claims-making—distribute organizational resources, rewards, and respect. The actual levels and contours of the inequalities produced by these three mechanisms are, however, profoundly contingent on the historical moments and institutional fields in which organizations operate. Organizational inequality regimes are comprised of the resources available for distribution; the task-, class-, and status-based social relations within organizations; formal and informal practices used to accomplish goals and tasks; and internal cultural models of people, work, and inequality, often adapted from the society at large to fit local social relationships. Legal and cultural institutions as they are filtered through workplace inequality regimes steer which groups are exploited and excluded, blocking or facilitating the conditions that lead to exploitation and closure. Sometimes exploitative and closure claims-making are naked and open for all to see; more often, they are institutionalized, taken for granted, and legitimated, sometimes even by those being exploited and excluded. The implications of RIT for social science and equality agendas are discussed in the conclusion. Case studies examine historical and contemporary workplace inequality regime variation in multiple countries. The role of intersectionality in producing regime variation is explored repeatedly across the book. Many occupations and industries are examined in depth, with particular attention given to engineers, CEOs, financial service, airlines, and information technology industries.

Americans wrote fiercely during their civil war. War surprised, devastated, and opened up imagination, taking hold of Americans’ words as well as their homes and families. The personal diary—wildly ragged yet rooted in day following day—was one place Americans wrote their war. Diaries, then, have become one of the best-known, most-used sources for exploring the life of the mind in a war-torn place and time. Delving into several familiar wartime diaries kept by women of the southern slave-owning class, Steven Stowe recaptures their motivations to keep the days close even as war tore apart the brutal system of slavery that had benefited them. Whether the diarists recorded thoughts about themselves, their opinions about men, or their observations about slavery, race, and warfare, Stowe shows how these women, by writing the immediate moment, found meaning in a changing world. In studying the inner lives of these unsympathetic characters, Stowe also explores the importance—and the limits—of historical empathy as a condition for knowing the past. He demonstrates how the plain, first-draft text of a diary can offer new ways to make sense of the world in which these Confederate women lived.

Ecocritique is a practice of radical questioning, as essential to the critical armoury as feminism and postcolonialism have become. Anecdotes are ecocritical because they focus on encounters, concentrated moments of crisis when social ordering and ecological forces clash. Bringing ecological criticism to bear on case studies of popular culture in the twenty-first century, Anecdotal Evidence argues that the humanities have a vital role to play in rethinking politics today. Treating contemporary Hollywood movies, streaming video media, and mass image databases as anecdotes about waste, debt, and obligation reveals the deep intertwining of history and ecology in culture. An original take on Anthropocene anxieties and technological paranoia, the book proposes that the digital humanities still need the traditional skills of close reading to understand our contemporary condition. Only because the environment has a history is it possible to intervene environmentally. Because we continually misrecognise the historical production of environments, the first task of ecocritique is to bring our formative concept of ecology into crisis. Its final task will be to achieve the good life for everything connected by the historical implication of humans in ecology, and ecology in humans. No politics can be undertaken in our times except through media: ecocritical humanities have a key role in rethinking ecopolitics in the twenty-first century.

Textures of the Ordinary: Doing Anthropology after Wittgenstein is an exploration of everyday life in which anthropology finds a companionship with philosophy. Based on two decades of ethnographic work among low-income urban families in India, Das shows how the notion of texture allows her to align her ethnography with stunning anthropological moments in Wittgenstein and Cavell as well as in literary texts from India. Das poses a compelling question—how might we speak of a human form of life when the very idea of the human has been put into question? The response to this question, Das argues, does not lie in some foundational idea of the universal as that of human nature or the human condition but in a close attention to the diverse ways in which the natural and the social mutually absorb each other within overlapping forms of life. The book shows how reality as ordinary and domestic is impaired not only by catastrophic events but also by the repetitive and corrosive soft knife of everyday violence and deprivation. It advances a view of ordinary ethics as attentiveness to the other and the ability of small acts of care to stand up to horrific violence. The book also presents a picture of thinking in which concepts and experience are shown to be mutually vulnerable and ethnography is treated as intimately connected to autobiography as a form of reflection emanating from the impersonal regions of the self.

Abstract“A single atomic particle forever floating at rest in free space” (H. Dehmelt) would be the ideal object for precision measurements of atomic properties and for tests of fundamental theories. Such an ideal, of course, can ultimately never be achieved. A very close approximation to this ideal is made possible by ion traps, where electromagnetic forces are used to confine charged particles under well-controlled conditions for practically unlimited time. Concurrently, sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to bring the trapped ion nearly to rest. Among different realisations of ion traps we consider in this chapter the so-called Penning traps which use static electric and magnetic fields for ion confinement. After a brief discussion of Penning-trap properties, we consider various experiments including the application of the “continuous Stern-Gerlach effect”, which have led recently to precise determinations of the masses and magnetic moments of particles and antiparticles. These serve as input for testing fundamental theories and symmetries.

Literary and cultural studies continue to navigate phases of intense methodological flux and disciplinary self-examination. The Introduction takes stock of the condition of close reading in modernist studies against the backdrop of this broader climate of change. It suggests that the rapport between close reading and the proliferating objects, elastic timeframes, and global contexts of modernist studies today no longer feels guaranteed. And it outlines some of the ways in which the volume will examine close reading’s history as an avenue to acquiring some sense of its futurity at a moment of unprecedented expansion and reconstitution for modernist scholarship.

A Conditional Moment Closure (CMC) approach embedded in an LES CFD framework is presented for simulation of the reactive flow field of an aero-engine combustor operating at altitude relight conditions. Before application to the combustor geometry, the CMC model was validated on the standard lab-scale Sandia flame D. For the combustor simulation, a global mechanism for n-heptane was used along with a Lagrangian approach for the spray, to which a secondary break-up model was applied. The simulation modelled a multi-sector sub-atmospheric rig that was used to verify the altitude relight capability of the combustor. A comprehensive suite of diagnostics was applied to the rig test, including high-speed OH and kerosene PLIF as well as high speed OH* chemiluminescence. The CMC-based CFD simulation was able to predict well the position of the flame front and fuel distribution at the low pressure, low temperature conditions typical of altitude relight. Furthermore, the simulation of the ignition showed strong similarities with OH* chemiluminescence measurements of the event. An EBU-based LES was run too and showed to be unable to capture the flame front as well as the CMC model could. This work demonstrates that CMC LES can be an effective tool to support assessment of the relight capability of aero-engine combustors.

Here the premixed Conditional Moment Closure (CMC) method is used to model the recent PIV and Raman turbulent, enclosed reacting methane jet data from DLR Stuttgart [1]. The experimental data has a rectangular test section at atmospheric pressure and temperature with a single inlet jet. A jet velocity of 90 m/s is used with an adiabatic flame temperature of 2,064 K. Contours of major species, temperature and velocities along with velocity rms values are provided. The conditional moment closure model has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes [2]. The simplified CMC model used here falls into the class of table lookup turbulent combustion models where the chemical kinetics are solved offline over a range of conditions and stored in a table that is accessed by the CFD code. Most table lookup models are based on the laminar 1-D flamelet equations, which assume the small scale turbulence does not affect the reaction rates, only the large scale turbulence has an effect on the reaction rates. The CMC model is derived from first principles to account for the effects of small scale turbulence on the reaction rates, as well as the effects of the large scale mixing, making it more versatile than other models. This is accomplished by conditioning the scalars with the reaction progress variable. By conditioning the scalars and accounting for the small scale mixing, the effects of turbulent fluctuations of the temperature on the reaction rates are more accurately modeled. The scalar dissipation is used to account for the effects of the small scale mixing on the reaction rates. The original premixed CMC model used a constant value of scalar dissipation, here the scalar dissipation is conditioned by the reaction progress variable. The steady RANS 3-D version of the open source CFD code OpenFOAM is used. Velocity, temperature and species are compared to the experimental data. Once validated, this CFD turbulent combustion model will have great utility for designing lean premixed gas turbine combustors.

This paper presents the premixed Conditional Moment Closure (CMC) method as a new tool for modeling turbulent premixed combustion with detailed chemistry. By using conditional averages the CMC method can more accurately model the affects of the turbulent fluctuations of the temperature on the reaction rates. This provides an improved means of solving a major problem with traditional turbulent reacting flow models, namely how to close the reaction rate source term. Combined with a commercial CFD code this model provides insight into the emission formation pathways with reasonable runtimes. Results using the full GRI2.11 methane kinetic mechanism are compared to experimental data for a backward facing step burning premixed methane. This model holds promise as a design tool for lean premixed gas turbine combustors.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.