Lec 8: Estimation of radiation in horizontal and inclined surface

Estimation of Solar Radiation

Overview of Today's Lesson

• The session focuses on estimating various types of solar radiation, including monthly averages for daily diffuse and global radiation, as well as the impact on tilted surfaces.

• A recap of previous discussions about the need for correlations in estimating radiations is provided. This includes classifications of weather conditions affecting radiation measurements.

Recap from Last Class

• Previous topics included calculations for monthly average daily extraterrestrial radiations and their application in determining global radiation.

• Emphasis was placed on understanding how different weather conditions (clear, cloudy, hazy) influence these estimations.

Monthly Average Diffuse Radiation

• The discussion introduces correlations developed by researchers like Liu and Jordan to relate monthly average diffuse radiation to global radiation using cubic expressions.

• Monthly average clearness index (KT) is defined as the ratio of terrestrial to extraterrestrial solar radiation, aiding in understanding diffuse versus global radiation ratios.

Correlations for Hourly Global Radiation

• Various correlations are presented for estimating hourly global beam and diffuse radiations under clear skies, highlighting the importance of location-specific models due to atmospheric variations.

• The ASHRAE model is introduced as a method for calculating global and diffuse radiation specifically for cloudless skies based on constants determined seasonally.

Detailed Calculation Methods

Understanding Beam and Diffuse Radiation

• Global radiation (IG) is defined as the sum of beam (IB) and diffuse (ID) components; formulas are provided to calculate these values based on known parameters like angle theta (θ).

• Constants A, B, C used in calculations vary by month due to seasonal changes affecting solar intensity; specific values are given for January through March.

Example Calculation: Guwahati Case Study

• An example calculation demonstrates how to estimate hourly global beam and diffuse radiation at a specific location with given latitude/longitude data over a specified time frame. Measurements are compared against actual data collected during that period.

Steps Involved:

1. Determine Latitude: Convert geographical coordinates into degrees.

2. Calculate Delta: Use established equations involving day number n to find solar declination angle.

3. Compute Cosine Values: Calculate cos θz using sine/cosine functions based on delta and phi angles at different times throughout the day.

4. Interpolation: For accurate results between months or days, interpolation methods are applied to derive constant values A, B, C needed in calculations.

Final Calculations & Results

Completing Calculations

• After deriving necessary cosine values at various hour angles (omega), IBN can be calculated using exponential functions involving constants A, B divided by cos θz leading to estimates in W/m² or kJ/m² per hour format depending on requirements outlined earlier in the lesson plan.

Key Findings:

1. Estimated IB values derived from IBN calculations yield significant insights into expected energy outputs from solar installations.

2. Comparison between predicted results versus measured data highlights discrepancies that necessitate localized adjustments in modeling approaches.

Conclusion & Implications

• The analysis concludes with an emphasis on needing tailored correlation models rather than universal ones due to varying atmospheric conditions across locations which affect solar energy capture efficiency significantly over time periods analyzed.

Solar Radiation Estimation on Tilted Surfaces

Introduction to Tilted Surface Analysis

• Transitioning from horizontal surface analysis, this section discusses how tilt affects received solar flux through three key components: beam radiation (IB), diffuse radiation (ID), and reflected radiance (RR). Specific tilt factors must be considered when analyzing inclined surfaces such as those found in photovoltaic systems or flat plate collectors used widely today.

Important Parameters:

1. Tilt Factor Definitions:

• Beam Radiation Tilt Factor R_B : Ratio comparing flux falling onto tilted vs horizontal surfaces.

• Diffuse Radiation Tilt Factor R_D : Defined under isotropic sky assumptions where uniform diffusion occurs across all angles relative towards ground level.

• Reflected Radiance R_R : Incorporates reflectivity effects impacting overall energy capture efficiency.

2. Mathematical Relationships:

• Formulas linking these factors allow practitioners to compute total incident energy accurately while accounting for environmental variables influencing performance metrics crucially important within renewable energy sectors today.

By following this structured approach throughout each segment discussed above ensures clarity while providing comprehensive insights into complex methodologies surrounding estimation techniques utilized within modern-day applications related directly back towards harnessing sustainable resources effectively moving forward!

Estimating Monthly Average Radiation on Inclined Surfaces

Monthly Average of Hourly Radiation

• To estimate the monthly average of hourly radiation flux received by an inclined surface, a specific formula is used: barR = R_B + I_D/I_G with appropriate adjustments for variables.

• The calculation requires consideration of the time interval, specifically evaluating at midpoints (e.g., 10:30 for 10:00 to 11:00). This ensures accuracy in angle evaluations.

Daily Variation of Solar Flux

• Researchers may also need to assess daily variations in solar flux, which can be calculated using another expression involving H_T and H_G . The formula incorporates daily radiation received by inclined surfaces.

• The equation simplifies to include terms like R_B + H_D/H_G + R_D + R_R , focusing on daily calculations.

Tilt Factor for Beam Radiation

• The tilt factor for beam radiation ( R_B ) is crucial when calculating daily radiation flux and involves integrating over time. It is expressed as R_B = cos(theta)/cos(theta_Z) .

• Integration involves trigonometric functions such as sine and cosine related to solar angles, requiring careful evaluation over specified intervals (sunrise to sunset).

Integration Process

• During integration, constants are factored out while variable components are integrated across defined limits (from sunrise to sunset), leading to expressions that combine sine and cosine terms effectively.

• Final results yield a comprehensive expression for R_B , incorporating both solar declination and local latitude adjustments based on surface tilt angles.

Monthly Average of Daily Radiation Calculations

Expression for Monthly Average Daily Radiation

• For estimating monthly averages of daily radiation, the expression combines various factors including hourly averages adjusted with respect to diffuse and reflected radiations. This leads to a comprehensive understanding of total energy received on tilted surfaces.

• Key parameters include H_T^b / H_G^b - I_D/I_G along with respective values for beam (R_B), diffuse (R_D), and reflected (R_R) radiations averaged over representative days.

Example Calculation Setup

• An example problem illustrates how to calculate monthly average hourly radiation falling on a flat plate collector installed at specific angles facing due south (gamma = 0°; slope = 26°). Location specifics are provided (New Delhi in October).

• Important parameters such as reflected radiation coefficient (ρ = 0.2) are established alongside direct normal irradiance values needed for calculations.

Detailed Calculation Steps

Declination Angle Calculation

• The calculation begins with determining the day number (n = 288) followed by computing the declination angle using standard formulas yielding approximately -9.599°. This step is critical in understanding solar position relative to Earth’s tilt during October days.

Latitude Consideration

• Latitude (phi) is calculated from geographical coordinates resulting in approximately 28°38'. This value plays a significant role in further calculations regarding solar angles impacting incident radiation on surfaces throughout the day.

Finalizing RB Value

• Using previously derived expressions, substituting known values allows computation of beam radiation factor (R_B ≈ 1.242). This value reflects how much direct sunlight impacts the tilted surface under given conditions at noon hours around midday (omega = ±7.5°).

Reflected Radiation Contribution

RD and RR Values

• Reflective contributions are assessed through equations yielding values like R_D ≈ 0.94393 based on surface inclination while considering factors like albedo effects from surrounding environments (grass surfaces typically have low reflectivity).

Application of Formulas

• Applying relationships between different types of radiative components enables researchers to derive total incident energy received by inclined surfaces accurately through systematic substitution into established formulas leading towards final results reflecting real-world scenarios effectively.

Summary Insights

Overview of Key Concepts Discussed

• Various correlations were explored concerning estimation methods for monthly average diffuse and global radiations applicable under different sky conditions emphasizing clear skies versus cloudy scenarios.

ASHRAE Model Utilization

• Discussion included insights into ASHRAE models developed specifically for estimating hourly global beam/diffuse radiations applicable primarily on horizontal surfaces under clear sky conditions highlighting their limitations regarding location-specific adaptations necessary for accurate predictions.

This structured approach provides clarity into complex discussions surrounding solar energy estimations while ensuring accessibility through organized notes linked directly back to relevant timestamps within the transcript content.