Podcast
Questions and Answers
In solar radiation calculations, what is the most reliable method for obtaining solar radiation values?
In solar radiation calculations, what is the most reliable method for obtaining solar radiation values?
- Calculating based on average sunshine hours.
- Actual equipment measurements. (correct)
- Using correlations proposed by researchers.
- Approximating from locations with similar solar conditions.
When actual solar radiation data is unavailable, which of the following is the next best alternative for estimating solar radiation values?
When actual solar radiation data is unavailable, which of the following is the next best alternative for estimating solar radiation values?
- Using the average sunshine hours of the location.
- Using the ASHRAE model.
- Using data from locations with similar solar conditions. (correct)
- Using correlations from Collares-Pereira, Rabi, and Guevmard.
What does ωs (omega s) signify in the context of solar radiation calculations for a horizontal surface?
What does ωs (omega s) signify in the context of solar radiation calculations for a horizontal surface?
- The hour angle at solar noon.
- The hour angle at which the solar radiation is maximum.
- The average hourly global radiation.
- The hour angle during sunrise or sunset. (correct)
In the Collares-Pereira and Rabi correlation for calculating monthly average hourly global radiation, which mathematical form is considered sufficient?
In the Collares-Pereira and Rabi correlation for calculating monthly average hourly global radiation, which mathematical form is considered sufficient?
In the context of diffusive radiation calculations, what do the Leon and Jordaa, and Satyamurty and Lahiri correlations have in common?
In the context of diffusive radiation calculations, what do the Leon and Jordaa, and Satyamurty and Lahiri correlations have in common?
When calculating the constant 'a' in diffusive radiation correlations, what condition determines which formula should be used?
When calculating the constant 'a' in diffusive radiation correlations, what condition determines which formula should be used?
In calculating hourly global, beam, and diffusive radiation under clear sky conditions using the ASHRAE model, what is the significance of constants A, B, and C?
In calculating hourly global, beam, and diffusive radiation under clear sky conditions using the ASHRAE model, what is the significance of constants A, B, and C?
When using the ASHRAE model, what conversion is required for constant A, and why?
When using the ASHRAE model, what conversion is required for constant A, and why?
In the context of radiation on tilted surfaces, what are the three components of total radiation, and how do they contribute to the total?
In the context of radiation on tilted surfaces, what are the three components of total radiation, and how do they contribute to the total?
What does the conversion factor Rb represent in the context of calculating radiation on tilted surfaces?
What does the conversion factor Rb represent in the context of calculating radiation on tilted surfaces?
How is the conversion factor Rd calculated when determining radiation on tilted surfaces?
How is the conversion factor Rd calculated when determining radiation on tilted surfaces?
If a concrete surface has a reflectivity (rho) of 0.2 and the tilt angle is 30 degrees, what is the value of the conversion factor Rr for radiation on tilted surfaces?
If a concrete surface has a reflectivity (rho) of 0.2 and the tilt angle is 30 degrees, what is the value of the conversion factor Rr for radiation on tilted surfaces?
In the formula for calculating daily radiation on tilted surfaces, what key difference distinguishes the calculation of Rb from that used for hourly radiation?
In the formula for calculating daily radiation on tilted surfaces, what key difference distinguishes the calculation of Rb from that used for hourly radiation?
When calculating daily radiation on a tilted surface, which parameters are required to determine the daily Rb ($\bar{r_b}$)?
When calculating daily radiation on a tilted surface, which parameters are required to determine the daily Rb ($\bar{r_b}$)?
What does the Local Apparent Time refer to?
What does the Local Apparent Time refer to?
Why is calculating the angle of incidence important in solar radiation studies?
Why is calculating the angle of incidence important in solar radiation studies?
What does Guevmard's modification to the Collares-Pereira and Rabi correlation involve?
What does Guevmard's modification to the Collares-Pereira and Rabi correlation involve?
Which parameter primarily influences the monthly variation in constants A, B, and C used in the ASHRAE clear sky model?
Which parameter primarily influences the monthly variation in constants A, B, and C used in the ASHRAE clear sky model?
How does increasing the tilt angle of a surface generally affect the amount of solar radiation it receives during the winter months in the northern hemisphere?
How does increasing the tilt angle of a surface generally affect the amount of solar radiation it receives during the winter months in the northern hemisphere?
If the ratio of diffuse to global radiation ($\frac{H_d}{H_g}$) is determined to be 0.8, which formula should be prioritized for calculating the constant 'a' in estimating diffuse solar radiation?
If the ratio of diffuse to global radiation ($\frac{H_d}{H_g}$) is determined to be 0.8, which formula should be prioritized for calculating the constant 'a' in estimating diffuse solar radiation?
Flashcards
Angle of Incidence
Angle of Incidence
The angle at which sunlight strikes a surface
Local Apparent Time (LAT)
Local Apparent Time (LAT)
Time corrected for the observer's longitude, used in solar radiation calculations.
Average Sunshine Hours
Average Sunshine Hours
Represents the average duration of sunshine in a month.
Omega (ωs)
Omega (ωs)
Signup and view all the flashcards
Monthly Average Hourly Diffusive Radiation (Id bar)
Monthly Average Hourly Diffusive Radiation (Id bar)
Signup and view all the flashcards
Ratio of Hd/Hg
Ratio of Hd/Hg
Signup and view all the flashcards
Hourly Global, Beam, and Diffusive Radiation
Hourly Global, Beam, and Diffusive Radiation
Signup and view all the flashcards
ASHRAE Model
ASHRAE Model
Signup and view all the flashcards
Cos(θz)
Cos(θz)
Signup and view all the flashcards
Hourly Beam Radiation (Ib)
Hourly Beam Radiation (Ib)
Signup and view all the flashcards
Rb
Rb
Signup and view all the flashcards
Rd
Rd
Signup and view all the flashcards
Rr
Rr
Signup and view all the flashcards
Tilted Surface Radiation
Tilted Surface Radiation
Signup and view all the flashcards
Cos(θi)
Cos(θi)
Signup and view all the flashcards
Rho (ρ)
Rho (ρ)
Signup and view all the flashcards
Study Notes
Solar Radiation Calculations
- The lecture focused on calculating nine solar radiation values.
Angle of Incidence
- The angle of incidence is a key value to calculate.
Local Apparent Time (LAT)
- Calculating LAT is necessary, especially concerning the Indian Standard Time (IST).
Monthly Average Daily and Hourly Radiation
- The problem also involved calculating monthly average daily and hourly global and diffusive radiation.
- Calculations initially focused on horizontal surfaces.
- The best method to obtain solar radiation values is through actual equipment measurements.
- When actual data is unavailable, locations with similar solar conditions can be used for approximations.
- If neither measurement nor similarity is feasible, correlations proposed by researchers can be employed.
- Average sunshine hours of 7.2 hours and an elevation of 14 meters above sea level were given.
- Monthly average hourly global radiation, denoted as Ig bar, was calculated using correlations from Collares-Pereira, Rabi, and Guevmard.
- Formula: Ig bar / I0 bar is proportional to Hg bar / H0 bar.
- Collares-Pereira and Rabi suggested that a + b cos(ω) is sufficient for calculations.
- Guevmard added a correction factor, fc, to better align with actual data.
- Omega (ωs) signifies the hour angle during sunrise or sunset for a horizontal surface.
- A monthly average hourly global radiation (Ig bar) value of 2182 kilojoules per meter squared per hour was found.
Diffusive Radiation
- Monthly average hourly diffusive radiation (Id bar) can be calculated.
- Correlation proposed by Leon and Jordaa: Id bar / Hd bar = I0 bar / H0 bar * (a + b cos ω).
- Satyamurty and Lahiri correlation: Id / Hd bar = I0 bar / H0 bar * (a + b cos ω).
- Constant 'a' can be calculated based on the ratio of Hd upon Hg.
- If the ratio of Hd/Hg is between 0.1 and 0.7, a specific formula should be used.
- If the ratio is between 0.7 and 0.9, another specific formula for 'a' should be used.
- 'b' is a function of 'a' and ωs (omega s).
- Omega s was previously calculated as 93.32 degrees or 1.628 radians.
- When the solar time is between 9 to 10 hours, ω (omega) is 37.5 degrees.
- I0 (solar radiation) was approximately 3871 kilojoules per meter squared per hour.
- Ig was calculated to be 2182 kilojoules per meter squared per hour.
- Hd was pre-calculated from Modi et al. and given in kilojoules per meter squared per day.
- H0 was calculated as 37957 kilojoules per meter squared per day.
- Hg bar was previously calculated.
- April 15th was chosen to equate I0 to I0 bar.
- Hd bar / Hg bar ratio was calculated as 9825 / 21213 = 0.4631.
- Using the first formula, 'a' = (4922 + 0.27) / 0.4631 = 1.0751
- A slight variation in calculation values is possible.
- 'b' is calculated as 2 * (1 - 1.0751) * sin(93.32 - 1.628) * cos(93.32) / (1.628 - 0.5) * sin(2 * 93.32) = -0.097.
- Substituting 'a' and 'b', Id = (3871 / 37957) * (1.0751 - 0.097 * cos(37.5)), resulting in approximately 999 kilojoules per meter squared per hour.
Hourly Global, Beam, and Diffusive Radiation Under Clear Sky
- Hourly global (Ig), beam (Ib), and diffusive radiation (Id) calculations were performed under clear sky conditions.
- ASHRAE (American Society of Heating, Refrigerating, and Air-Conditioning Engineers) model was used.
- The ASHRAE model was originally based on US data.
- The model requires constants A, B, and C, which vary each month.
- Constants differ monthly due to changes in climatic conditions, water vapor content, atmospheric dust, and the Earth-Sun position.
- Constants A, B, and C were provided for April 21st.
- Constant A is given in flux watts per meter squared and must be converted to kilojoules per meter squared per hour.
- Conversion involves multiplying by 3600 and dividing by 1000.
- Constants B and C are unitless.
- The beta value is unnecessary because calculations are performed for horizontal surfaces only.
- Omega (ω) is 37.5 degrees for the 9-10 hour interval.
- Delta (δ) is calculated for April 21st, the 111th day of the year.
- Cos(θz) is calculated as sin(19.28) * sin(11.57) + cos(19.28) * cos(11.57) * cos(37.5) = 0.7998.
- Hourly beam radiation (Ib) is equivalent to Ibn * cos(θz).
- ASHRAE model is used to calculate Ibn: A * e^(-b / cos(θz)).
- For A = 4068 and B = 0.164, Ibn = 4068 * e^(-0.164 / 0.7998) = 3314 kilojoules per meter squared per hour.
- Using the value, Ib = 3314 * 0.7998 = 2650 kilojoules per meter squared per hour.
- I d is calculated as C * I bn = 0.120 * 3314 = 397 kilojoules per meter squared per hour.
- Ig can be found by adding Ib and Id.
- The value found was Ig = 2650 + 397 = 3048 kilojoules per meter squared per hour.
Radiation on Tilted Surfaces
- Total radiation falling on a tilted surface is calculated as: Ib * Rb + Id * Rd + Ig * Rr.
- To convert the formula, divide throughout by Ig.
- Re-written: (Ig - Id) / Ig * Rb + Id / Ig * Rd + Rr.
- The conversion factors Rb, Rd, and Rr are needed.
- Rb is calculated as cos(θi) / cos(θz).
- Cos(θi) = sin(δ) * sin(latitude - tilt) + cos(δ) * cos(ω) * cos(latitude - tilt).
- Cos(θz) = sin(latitude) * sin(δ) + cos(latitude) * cos(δ) * cos(ω).
- If these are calculated, the found value is approximately 0.9316.
- Rd is calculated as (1 + cos(tilt)) / 2 = 0.9330 for a 30 degree tilt.
- Rr is calculated as rho * (1 - cos(tilt)) / 2 = 0.2 * (1 - cos(30)) / 2 = 0.0133, assuming rho (reflectivity) is 0.2 for concrete surfaces.
- Substitute into equation: It / Ig = (1 - Id / Ig) * Rb + Id / Ig * Rd + Rr. Ig = 2182, Rb = 0.9316, Id = 999, Rd = 0.933, Rr = 0.0133
- Substitute and you find that IT is equal to 2063 kilojoules per meter squared per hour.
Daily Basis Calculation (tilted surfaces)
- Formula for daily basis: Ht / Hg = (1 - Hd / Hg) * Rb + Hd / Hg * Rd + Rr.
- The calculation of Rb is different for daily basis.
- Omega st and omega s factor in more distinctively.
- With omega st is 88.20 degrees and omega s is 93.32 degrees.
- Daily Rb = (cos(latitude - tilt)cos(delta)cos(omega_st))/(cos(latitude)cos(delta)cos(omega_s)).
- Omega st is 1.539 sin (19.28 - 30) sin 9.42 cos 9.42 sin 88.20 , then cos(19.28 -30)
- Omega s is 1.628 sin sin(19.28)sin(9.42) + (cos (19.28)cos(9.42)cos (37.5) sin 93.3.
- r b is calculated as 1.11.
- Rd is same as previously calculated which is 0.933.
- Rr is also the same at 0.0133.
- Ht bar / Hg bar = (1 - Hd bar / Hg bar) * rb bar + (Hd bar / Hg bar) * rd bar + Rr bar.
- hd is equal to 9825 and hg is eqaul to 21213.
- Ht ends up being 22089kJ per day
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
