1. K. B. Sutar, M. Ilyash, S. Kohli* & M. R. Ravi Department of Mechanical Engineering Indian Institute of Technology Delhi, India Department of Mechanical Engineering Indian Institute of Technology Delhi, India

2.  Introduction  Methodology used  Uncertainty in cookstove testing  Results of tests on cookstoves  Implication of the analysis on protocol design  Introduction  Methodology used  Uncertainty in cookstove testing  Results of tests on cookstoves  Implication of the analysis on protocol design

3.  Testing of stoves continues to be an important area for scientists and researchers area for scientists and researchers  Two conflicting requirements of a good testing protocol: protocol: Repeatability in the lab measurements Repeatability in the lab measurements Need for the test results to be representative of the Need for the test results to be representative of the field performance field performance  Testing of stoves continues to be an important area for scientists and researchers area for scientists and researchers  Two conflicting requirements of a good testing protocol: protocol: Repeatability in the lab measurements Repeatability in the lab measurements Need for the test results to be representative of the Need for the test results to be representative of the field performance field performance

4.  The approach suggested by K. Krishna Prasad (1985) to resolve the conflict (1985) to resolve the conflict Ensuring repeatable measurements in lab. Ensuring repeatable measurements in lab. Determining efficiency (η) versus fire power (P) as Determining efficiency (η) versus fire power (P) as performance characteristics. performance characteristics. Combination of the above can be used for performance Combination of the above can be used for performance prediction in the field. prediction in the field.  Focus of the present work Identifying the main contributors to the high uncertainty in Identifying the main contributors to the high uncertainty in cookstove test results with a view to improve repeatability. cookstove test results with a view to improve repeatability. Developing a methodology for obtaining η Vs P curve Developing a methodology for obtaining η Vs P curve  The approach suggested by K. Krishna Prasad (1985) to resolve the conflict (1985) to resolve the conflict Ensuring repeatable measurements in lab. Ensuring repeatable measurements in lab. Determining efficiency (η) versus fire power (P) as Determining efficiency (η) versus fire power (P) as performance characteristics. performance characteristics. Combination of the above can be used for performance Combination of the above can be used for performance prediction in the field. prediction in the field.  Focus of the present work Identifying the main contributors to the high uncertainty in Identifying the main contributors to the high uncertainty in cookstove test results with a view to improve repeatability. cookstove test results with a view to improve repeatability. Developing a methodology for obtaining η Vs P curve Developing a methodology for obtaining η Vs P curve

5.  A commercially available forced draught stove with fan regulator was tested using BIS (with minor fan regulator was tested using BIS (with minor modifications), WBT 3.0 and EPTP protocols. modifications), WBT 3.0 and EPTP protocols.  Each test was repeated three to four times.  Only thermal performance was measured (No emission measurements). emission measurements).  Detailed uncertainty analysis was carried out to identify the main contributors to uncertainty. identify the main contributors to uncertainty.  Steps identified to reduce the uncertainty  A commercially available forced draught stove with fan regulator was tested using BIS (with minor fan regulator was tested using BIS (with minor modifications), WBT 3.0 and EPTP protocols. modifications), WBT 3.0 and EPTP protocols.  Each test was repeated three to four times.  Only thermal performance was measured (No emission measurements). emission measurements).  Detailed uncertainty analysis was carried out to identify the main contributors to uncertainty. identify the main contributors to uncertainty.  Steps identified to reduce the uncertainty

6.  Source of uncertainty due to measuring instruments due to inherent variability in the basic phenomena (combustion, heat transfer, etc.) and method of conducting experiments Baldwin (1988) first reported statistical analysis using student's t-test in cookstove testing.  Source of uncertainty due to measuring instruments due to inherent variability in the basic phenomena (combustion, heat transfer, etc.) and method of conducting experiments Baldwin (1988) first reported statistical analysis using student's t-test in cookstove testing.

7. Let,  1,  2,  3 …….  n be the efficiencies at cold start phase Let,  1,  2,  3 …….  n be the efficiencies at cold start phase of WBT for the cookstove. of WBT for the cookstove. Arithmetic mean of efficiency, Arithmetic mean of efficiency, Unbiased or sample standard deviation Unbiased or sample standard deviation Confidence interval gives the probability that the mean Confidence interval gives the probability that the mean value of efficiency lies within a certain number (t) of value of efficiency lies within a certain number (t) of sample standard deviation (s) which gives, sample standard deviation (s) which gives, Let,  1,  2,  3 …….  n be the efficiencies at cold start phase Let,  1,  2,  3 …….  n be the efficiencies at cold start phase of WBT for the cookstove. of WBT for the cookstove. Arithmetic mean of efficiency, Arithmetic mean of efficiency, Unbiased or sample standard deviation Unbiased or sample standard deviation Confidence interval gives the probability that the mean Confidence interval gives the probability that the mean value of efficiency lies within a certain number (t) of value of efficiency lies within a certain number (t) of sample standard deviation (s) which gives, sample standard deviation (s) which gives,

8. The variable t, for different degrees of freedom (n- 1) and levels of confidence can be found in the tables available in literature on statistics. The number of degrees of freedom is given by, = n-1. For example, at 95% confidence interval and at n = 3 i.e. for = 2, the value of t is 4.303. The variable t, for different degrees of freedom (n- 1) and levels of confidence can be found in the tables available in literature on statistics. The number of degrees of freedom is given by, = n-1. For example, at 95% confidence interval and at n = 3 i.e. for = 2, the value of t is 4.303.

9. Tests were conducted using Tests were conducted using modified BIS protocol. modified BIS protocol. Cookstove was run at different Cookstove was run at different fire powers by regulating fan fire powers by regulating fan speed and corresponding fuel speed and corresponding fuel burning rate. burning rate. Each test was conducted Each test was conducted thrice. thrice. Tests were conducted using Tests were conducted using modified BIS protocol. modified BIS protocol. Cookstove was run at different Cookstove was run at different fire powers by regulating fan fire powers by regulating fan speed and corresponding fuel speed and corresponding fuel burning rate. burning rate. Each test was conducted Each test was conducted thrice. thrice. Maximum stove efficiency in the range of 2.3 kW to 3.5 kW fire power.

10. To determine whether the test should end: To determine whether the test should end: when the water reaches at a specified temperature (WBT 3.0) or when when the water reaches at a specified temperature (WBT 3.0) or when the fuel burns completely (BIS). the fuel burns completely (BIS). To determine whether the test should end: To determine whether the test should end: when the water reaches at a specified temperature (WBT 3.0) or when when the water reaches at a specified temperature (WBT 3.0) or when the fuel burns completely (BIS). the fuel burns completely (BIS). WBT shows higher uncertainty in thermal performance than BIS WBT shows higher uncertainty in thermal performance than BIS WBT results must be reported separately for different phases: WBT results must be reported separately for different phases: (cold start, hot start and simmering) WBT shows higher uncertainty in thermal performance than BIS WBT shows higher uncertainty in thermal performance than BIS WBT results must be reported separately for different phases: WBT results must be reported separately for different phases: (cold start, hot start and simmering)

11. Efficiency of the cookstove, η = f (m i, m f, T i, T f, m b, m c, CV b, CV c ) Efficiency of the cookstove, η = f (m i, m f, T i, T f, m b, m c, CV b, CV c ) Uncertainties in masses of water, biomass and charcoal and temperatures of Uncertainties in masses of water, biomass and charcoal and temperatures of water viz. dm i, dm f, dm c, dm b (kg); dT i, dT f (  C); CV b, CV c (kJ/kg) water viz. dm i, dm f, dm c, dm b (kg); dT i, dT f (  C); CV b, CV c (kJ/kg) Efficiency of the cookstove,  = E out /E in Efficiency of the cookstove,  = E out /E in Differential uncertainty, Differential uncertainty, Where, Where, Energy supplied by combustion of fuel, E in = m b CV b – m c CV c Energy supplied by combustion of fuel, E in = m b CV b – m c CV c Differential uncertainty in energy supplied, Differential uncertainty in energy supplied, Efficiency of the cookstove, η = f (m i, m f, T i, T f, m b, m c, CV b, CV c ) Efficiency of the cookstove, η = f (m i, m f, T i, T f, m b, m c, CV b, CV c ) Uncertainties in masses of water, biomass and charcoal and temperatures of Uncertainties in masses of water, biomass and charcoal and temperatures of water viz. dm i, dm f, dm c, dm b (kg); dT i, dT f (  C); CV b, CV c (kJ/kg) water viz. dm i, dm f, dm c, dm b (kg); dT i, dT f (  C); CV b, CV c (kJ/kg) Efficiency of the cookstove,  = E out /E in Efficiency of the cookstove,  = E out /E in Differential uncertainty, Differential uncertainty, Where, Where, Energy supplied by combustion of fuel, E in = m b CV b – m c CV c Energy supplied by combustion of fuel, E in = m b CV b – m c CV c Differential uncertainty in energy supplied, Differential uncertainty in energy supplied,

12. Energy utilized for boiling of water, E out = m i C p,w (T f – T i ) + (m i - m f )h fg Energy utilized for boiling of water, E out = m i C p,w (T f – T i ) + (m i - m f )h fg Differential uncertainty in energy utilized, Differential uncertainty in energy utilized, Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Contributions to uncertainty in thermal efficiency : (29.95  7.96)% Contributions to uncertainty in thermal efficiency : (29.95  7.96)% Energy utilized for boiling of water, E out = m i C p,w (T f – T i ) + (m i - m f )h fg Energy utilized for boiling of water, E out = m i C p,w (T f – T i ) + (m i - m f )h fg Differential uncertainty in energy utilized, Differential uncertainty in energy utilized, Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Contributions to uncertainty in thermal efficiency : (29.95  7.96)% Contributions to uncertainty in thermal efficiency : (29.95  7.96)%

13. Fire power of the cookstove, P = f (m b, m c, CV b, CV c, t)also P = E in /t Fire power of the cookstove, P = f (m b, m c, CV b, CV c, t)also P = E in /t Differential uncertainty in fire power, Differential uncertainty in fire power,Where, Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Contributions to uncertainty in fire power: (2.94  1.52) kW Contributions to uncertainty in fire power: (2.94  1.52) kW Fire power of the cookstove, P = f (m b, m c, CV b, CV c, t)also P = E in /t Fire power of the cookstove, P = f (m b, m c, CV b, CV c, t)also P = E in /t Differential uncertainty in fire power, Differential uncertainty in fire power,Where, Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water. Contributions to uncertainty in fire power: (2.94  1.52) kW Contributions to uncertainty in fire power: (2.94  1.52) kW

14. About 92 % of the uncertainty in efficiency is contributed by the About 92 % of the uncertainty in efficiency is contributed by the uncertainty in the final mass of water. uncertainty in the final mass of water. Water should not be allowed to vaporize, i.e. heat the water Water should not be allowed to vaporize, i.e. heat the water well below boiling point and use a pot lid. well below boiling point and use a pot lid. To reduce uncertainty in fire power, fuel should be consumed fully To reduce uncertainty in fire power, fuel should be consumed fully or till only charcoal is left. or till only charcoal is left. Leftover charcoal must be accounted for. Leftover charcoal must be accounted for. About 92 % of the uncertainty in efficiency is contributed by the About 92 % of the uncertainty in efficiency is contributed by the uncertainty in the final mass of water. uncertainty in the final mass of water. Water should not be allowed to vaporize, i.e. heat the water Water should not be allowed to vaporize, i.e. heat the water well below boiling point and use a pot lid. well below boiling point and use a pot lid. To reduce uncertainty in fire power, fuel should be consumed fully To reduce uncertainty in fire power, fuel should be consumed fully or till only charcoal is left. or till only charcoal is left. Leftover charcoal must be accounted for. Leftover charcoal must be accounted for. Rather than heating fixed quantity of water to a fixed temperature, Rather than heating fixed quantity of water to a fixed temperature, it is better to burn a fixed quantity of fuel completely and transfer it is better to burn a fixed quantity of fuel completely and transfer heat to vessels with known quantity of water. heat to vessels with known quantity of water. Rather than heating fixed quantity of water to a fixed temperature, Rather than heating fixed quantity of water to a fixed temperature, it is better to burn a fixed quantity of fuel completely and transfer it is better to burn a fixed quantity of fuel completely and transfer heat to vessels with known quantity of water. heat to vessels with known quantity of water.

15. Tests conducted on cookstove using WBT 3.0 protocol. Tests conducted on cookstove using WBT 3.0 protocol. Higher stove efficiency for vessel with 5L as compared to that with 2.5L. Fire power should be independent of quantity of water. Fire power should be independent of quantity of water. To know the reason behind lower fire power during 2.5L WBT, more To know the reason behind lower fire power during 2.5L WBT, more tests required to be conducted. tests required to be conducted. Higher stove efficiency for vessel with 5L as compared to that with 2.5L. Fire power should be independent of quantity of water. Fire power should be independent of quantity of water. To know the reason behind lower fire power during 2.5L WBT, more To know the reason behind lower fire power during 2.5L WBT, more tests required to be conducted. tests required to be conducted.

16. Tests conducted on cookstove using EPTP protocol at different fuel feeding rates. Tests conducted on cookstove using EPTP protocol at different fuel feeding rates. No clear conclusion can be drawn due to large uncertainties associated with the results. Need for more tests. No clear conclusion can be drawn due to large uncertainties associated with the results. Need for more tests. In general, feeding the fuel disturbs the combustion, and larger the feed, greater is the disturbance i.e. lower uncertainty is expected for continuous feed. In general, feeding the fuel disturbs the combustion, and larger the feed, greater is the disturbance i.e. lower uncertainty is expected for continuous feed.

17. This statistical technique can be used to identify the better one from a pair of samples subjected to identical operating conditions. This statistical technique can be used to identify the better one from a pair of samples subjected to identical operating conditions. Let X i and Y i be the efficiencies of cookstove at X and Y feeding rates respectively for i th test. Let X i and Y i be the efficiencies of cookstove at X and Y feeding rates respectively for i th test. (X 1,Y 1 ), (X 2,Y 2 )……..(X n, Y n ) be the n pairs of the efficiency data. (X 1,Y 1 ), (X 2,Y 2 )……..(X n, Y n ) be the n pairs of the efficiency data. Let D i = X i –Y i … difference between the efficiencies for i th test. Let D i = X i –Y i … difference between the efficiencies for i th test. Let D 1,…. D i …. D n be a small random sample of differences of pairs. Let D 1,…. D i …. D n be a small random sample of differences of pairs. If the number n is small (<30), then the level 100(1-  )% confidence If the number n is small (<30), then the level 100(1-  )% confidence interval for the mean difference  D is given by interval for the mean difference  D is given by Let X i and Y i be the efficiencies of cookstove at X and Y feeding rates respectively for i th test. Let X i and Y i be the efficiencies of cookstove at X and Y feeding rates respectively for i th test. (X 1,Y 1 ), (X 2,Y 2 )……..(X n, Y n ) be the n pairs of the efficiency data. (X 1,Y 1 ), (X 2,Y 2 )……..(X n, Y n ) be the n pairs of the efficiency data. Let D i = X i –Y i … difference between the efficiencies for i th test. Let D i = X i –Y i … difference between the efficiencies for i th test. Let D 1,…. D i …. D n be a small random sample of differences of pairs. Let D 1,…. D i …. D n be a small random sample of differences of pairs. If the number n is small (<30), then the level 100(1-  )% confidence If the number n is small (<30), then the level 100(1-  )% confidence interval for the mean difference  D is given by interval for the mean difference  D is given by

18.  The effect of fuel feeding rate in WBT on cookstove efficiency : Pairs compared: (continuous feed Vs 100g) Pairs compared: (continuous feed Vs 100g) (continuous feed Vs 50g) (100g Vs 50g)  The effect of fuel feeding rate in WBT on cookstove efficiency : Pairs compared: (continuous feed Vs 100g) Pairs compared: (continuous feed Vs 100g) (continuous feed Vs 50g) (100g Vs 50g)  Comparison between 100g and 50g fuel feeing rates n = 4Cold Start Hot Start Simmering WBT Cycle η 100g (X)27.8323.0335.2628.84 η 50g (Y)21.4327.3632.8927.35 Diff. (D = X-Y)6.41-4.332.371.49 1.484 Sample Std. Dev. s D 4.427 t n-1, 0.025 3.182 t n-1, 0.025 s D /sqrt(n)7.043  D @ 95% CI 1.484  7.043 i.e. (-5.559, +8.527) At 95% CI, mean difference in efficiencies is more on positive side hence efficiency of cookstove is better with 100g fuel feeding rate than with 50g fuel feeding rate. At 95% CI, mean difference in efficiencies is more on positive side hence efficiency of cookstove is better with 100g fuel feeding rate than with 50g fuel feeding rate.

19.  Comparison between continuous and 50g fuel feeing rates n = 4Cold StartHot StartSimmeringWBT Cycle η continuous (X)26.8629.0732.3829.78 η 50g (Y)21.4327.3632.8927.35 Difference (D = X - Y)5.431.71-0.512.43 2.266 Sample Standard Dev. s D 2.451 t n-1, 0.025 3.182 t n-1, 0.025 s D /sqrt(n)3.900  D @ 95% CI (2.266  3.9 ) i.e. (+6.165, -1.634) At 95% CI, mean difference in efficiencies is more on positive side hence efficiency of cookstove is better with continuous fuel feeding rate than with 50g fuel feeding rate. At 95% CI, mean difference in efficiencies is more on positive side hence efficiency of cookstove is better with continuous fuel feeding rate than with 50g fuel feeding rate.

20.  Comparison between continuous and 100g fuel feeing rates n = 4Cold StartHot StartSimmeringWBT Cycle η continuous (X)26.8629.0732.3829.78 η 50g (Y)27.8323.0335.2628.84 Difference (D = X - Y)-0.986.04-2.870.94 0.782 Sample Standard Dev. s D 3.835 t n-1, 0.025 3.182 t n-1, 0.025 s D /sqrt(n)6.101  D @ 95% CI (0.782  6.101 ) i.e. (6.883, -5.319) At 95% CI, mean difference in efficiencies is slightly on positive side hence efficiency of cookstove is marginally better with continuous fuel feeding rate than with 100g fuel feeding rate. At 95% CI, mean difference in efficiencies is slightly on positive side hence efficiency of cookstove is marginally better with continuous fuel feeding rate than with 100g fuel feeding rate.

21.  Uncertainty in cookstove performance data can be minimized: minimized: by not allowing water to vaporize, and by using a lid during testing. by not allowing water to vaporize, and by using a lid during testing. by completely consuming the fuel, and accounting for any remaining by completely consuming the fuel, and accounting for any remaining charcoal. charcoal.  Uncertainty in cookstove performance data can be minimized: minimized: by not allowing water to vaporize, and by using a lid during testing. by not allowing water to vaporize, and by using a lid during testing. by completely consuming the fuel, and accounting for any remaining by completely consuming the fuel, and accounting for any remaining charcoal. charcoal.  Statistical analysis of stove test data helps in identifying the largest contributor(s) to the uncertainty and hence identifying the largest contributor(s) to the uncertainty and hence minimizing the contributions(s) minimizing the contributions(s) comparing the influence of different parameters on the cookstove comparing the influence of different parameters on the cookstove performance. performance.  Statistical analysis of stove test data helps in identifying the largest contributor(s) to the uncertainty and hence identifying the largest contributor(s) to the uncertainty and hence minimizing the contributions(s) minimizing the contributions(s) comparing the influence of different parameters on the cookstove comparing the influence of different parameters on the cookstove performance. performance.  Feasibility of determining η Vs P characteristics for the stove has been demonstrated