K. B. Sutar, M. Ilyash, S. Kohli* & M. R. Ravi
Department of Mechanical Engineering
Indian Institute of Technology
Delhi, India
Introduction
Methodology used
Uncertainty in cookstove testing
Results of tests on cookstoves
Implication of the analysis on protocol design
Testing of stoves continues to be an important
area for scientists and researchers
Two conflicting requirements of a good testing
protocol:
•Repeatability in the lab measurements
•Need for the test results to be representative of the
field performance
The approach suggested by K. Krishna Prasad
(1985) to resolve the conflict
•Ensuring repeatable measurements in lab.
•Determining efficiency (η) versus fire power (P) as
performance characteristics.
•Combination of the above can be used for performance
prediction in the field.
Focus of the present work
•Identifying the main contributors to the high uncertainty in
cookstove test results with a view to improve repeatability.
•Developing a methodology for obtaining η Vs P curve
A commercially available forced draught stove with
fan regulator was tested using BIS (with minor
modifications), WBT 3.0 and EPTP protocols.
Each test was repeated three to four times.
Only thermal performance was measured (No
emission measurements).
Detailed uncertainty analysis was carried out to
identify the main contributors to uncertainty.
Steps identified to reduce the uncertainty
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.
•Let, 1, 2, 3…….n be the efficiencies at cold start phase
of WBT for the cookstove.
•Arithmetic mean of
 1   2  .....   n 

n


efficiency,  
•Unbiased or sample standard deviation
1/ 2
 n (i  m ) 2 
s  

 i 1 (n  1) 
•Confidence interval gives the probability that the mean
value of efficiency lies within a certain number (t) of
sample standard deviation (s) which gives,
   
tn 1, / 2 s
n
[at (1- )  100% confidence level]
•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.
•Tests were conducted using
modified BIS protocol.
•Cookstove was run at different
fire powers by regulating fan
speed and corresponding fuel
burning rate.
•Each test was conducted
thrice.
Maximum stove efficiency in the range of 2.3 kW to
3.5 kW fire power.
•To determine whether the test should end:
• when the water reaches at a specified temperature (WBT 3.0) or when
the fuel burns completely (BIS).
• WBT shows higher uncertainty in thermal performance than BIS
• WBT results must be reported separately for different phases:
(cold start, hot start and simmering)
•Efficiency of the cookstove, η = f (mi, mf, Ti, Tf, mb, mc, CVb, CVc)
•Uncertainties in masses of water, biomass and charcoal and temperatures of
water viz. dmi, dmf, dmc, dmb (kg); dTi, dTf (C); CVb, CVc (kJ/kg)
•Efficiency of the cookstove,  = Eout/Ein
•Differential uncertainty,
•Where,

1

Eout Ein
1/ 2
2
2
 

 
 
d  
dEout   
dEin  

E

E

out
in


 


 Eout


Ein
Ein 2
•Energy supplied by combustion of fuel, Ein = mbCVb – mcCVc
•Differential uncertainty in energy supplied,
1/2
2
2
2
2
 E
  Ein
  Ein
  Ein
 
in
dEin  
dmb   
dCVb   
dmc   
dCVc  
 mb
  CVb
  mc
  CVc
 
•Energy utilized for boiling of water, Eout = miCp,w(Tf – Ti) + (mi - mf)hfg
•Differential uncertainty in energy utilized,
dEout
2 1/2
 E
  Eout
 
  Eout
  Eout
out
 
dmi   
dTi   
dT f   
dm f  
 T f
  m f
 
Ti
 mi






 

2
2
2
•Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water.
•Contributions to uncertainty in thermal efficiency : (29.95  7.96)%
•Fire power of the cookstove, P = f (mb, mc, CVb, CVc, t) also P = Ein/t
•Differential uncertainty in fire power,
1/2
2
2
 P
  P  
dP  
dEin   
dt  
 
 Ein
  t
Where,
P
1

Ein t
P  Ein
 2
t
t
•Experiment: Cold Start Phase, WBT: Vessel with 2.5 Liters of water.
•Contributions to uncertainty in fire power: (2.94  1.52) kW
•About 92 % of the uncertainty in efficiency is contributed by the
uncertainty in the final mass of water .
•Water should not be allowed to vaporize, i.e. heat the water
well below boiling point and use a pot lid.
•To reduce uncertainty in fire power, fuel should be consumed fully
or till only charcoal is left.
•Leftover charcoal must be accounted for.
•Rather than heating fixed quantity of water to a fixed temperature,
it is better to burn a fixed quantity of fuel completely and transfer
heat to vessels with known quantity of water.
•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.
•To know the reason behind lower fire power during 2.5L WBT, more
tests required to be conducted.
•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.
•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.
•This statistical technique can be used to identify the better one from a
pair of samples subjected to identical operating conditions.
•Let Xi and Yi be the efficiencies of cookstove at X and Y feeding rates
respectively for ith test.
•(X1,Y1), (X2,Y2)……..(Xn, Yn) be the n pairs of the efficiency data.
•Let Di = Xi –Yi … difference between the efficiencies for ith test.
•Let D1,…. Di…. Dn be a small random sample of differences of pairs.
•If the number n is small (<30), then the level 100(1-)% confidence
interval for the mean difference D is given by D  D  tn1, /2
sD
n
The effect of fuel feeding rate in WBT on cookstove efficiency :
•Pairs compared: (continuous feed Vs 100g)
(continuous feed Vs 50g)
(100g Vs 50g)
Comparison between 100g and 50g fuel feeing rates
n=4
Cold Start
η100g (X)
η50g (Y)
Diff. (D = X-Y)
D
27.83
21.43
6.41
Hot
WBT
Simmering
Start
Cycle
23.03
35.26
28.84
27.36
32.89
27.35
-4.33
2.37
1.49
1.484
Sample Std. Dev. sD
4.427
tn-1, 0.025
3.182
tn-1, 0.025sD/sqrt(n)
D @ 95% CI
7.043
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.
Comparison between continuous and 50g fuel feeing rates
n=4
Cold Start
Hot Start
Simmering
WBT Cycle
ηcontinuous (X)
η50g (Y)
Difference (D = X - Y)
26.86
21.43
5.43
29.07
27.36
1.71
32.38
32.89
-0.51
29.78
27.35
2.43
D
2.266
Sample Standard Dev. sD
2.451
tn-1, 0.025
3.182
tn-1, 0.025sD/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.
Comparison between continuous and 100g fuel feeing rates
n=4
Cold Start
Hot Start
Simmering
WBT Cycle
ηcontinuous (X)
η50g (Y)
Difference (D = X - Y)
26.86
27.83
-0.98
29.07
23.03
6.04
32.38
35.26
-2.87
29.78
28.84
0.94
D
0.782
Sample Standard Dev. sD
3.835
tn-1, 0.025
3.182
tn-1, 0.025sD/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.
Uncertainty in cookstove performance data can be
minimized:
•by not allowing water to vaporize, and by using a lid during testing.
•by completely consuming the fuel, and accounting for any remaining
charcoal.
Statistical analysis of stove test data helps in
•identifying the largest contributor(s) to the uncertainty and hence
minimizing the contributions(s)
•comparing the influence of different parameters on the cookstove
performance.
Feasibility of determining η Vs P characteristics for the stove has
been demonstrated